Possibly; that's what I'm trying to determine. The way that magic has become more pervasive within some of the classes makes me question it, but the modular nature of the game may make for better support (if more effort on my part to fill in the missing pieces).
I'll explain how I interpret the magic level based on the sparse magic feeling you seem to be aiming for.
5e Pros:
-No assumption of magic items--you can literally play the game without magic items
at all, and the math works out. There are some monsters that are resistant or immune to non-magical weapons, which makes for some interesting experiences of creativity, and puts the fear of the supernatural into the world.
-It includes the non-magical classes you've come to expect from 2e: Fighter and Rogue. They each have 2 subclasses to choose from (they each have an additional magic-using one, which you simply disallow). Fighter has a simple Champion for the same feel you've come to expect, plus the Battle Master which lets you use combat maneuvers. Battle Master is
great for a low-magic (or even no-magic campaign) because it lets you custom design fighters with a variety of completely Magic Free™ combat styles. You can make a swashbuckler who disarms and ripostes, a gladiator who tosses people around the battlefield, or a tactical leader who can call out commands to allies. And if there are any maneuvers you dislike, you just cross them off of the campaign options. Rogue comes in Thief and Assassin flavors, and the only magic they have is that Thief can read scrolls, I mean use magical devices, at a high level. Plus, you get the Barbarian (Berserker) as a bonus non-magical class!
-They've tried to put more wonder than numbers into magical items. For example, some magic weapons and armor don't even give you +s (and the highest + is +3), they just give you some cool special ability instead. So the magic items you do find will feel more "magical."
5e Cons:
-Most caster classes have at-will cantrips. This is something you can houserule out, but you'd have to decide how you want to do it--there isn't just an obvious "cross it off the options" solution.
-By default, absurdly easy to identify magical items. The DMG has a variant rule for that.
-Bards are full-casters. No simple fix for that.
-Paladins and rangers get spellcasting at 2nd-level. Ditto (although you can find official rules for a non-magical ranger
here).
So the summary is that you can basically play exactly the level of magic it sounds like you want if you house-rule how cantrips and item identification work. You'd also want to disallow the Magic Initiate feat, and maybe the Ritual Caster feat (though you might actually like that one).
That doesn't address bards and paladins, but that is a class issue rather than an overall sparsity of magic issue.
I don't seem to recall ability modifiers or leveling of ability scores being in any edition prior to 3.0, so no, it's just criticism of elements from more recent editions.
I agree that the way they established ability modifiers in 3e is somewhat unfortunate. Note however, that they only standardized the numbers which had been there since 1e and BECMI. The major advantage of 2e is that you used your entire ability score for ability/proficiency checks. The disadvantage of that method is that the roll-under situation makes it unwieldy--especially when you are dealing with supernaturally high scores.
As far as getting to increase your ability scores as you level up, there are two points to that. The first is that your scores are capped at 20, and the second is that the math works a little differently. You don't
have to have a high score in your primary ability scores like you did in 3e and 4e. If you want your fighter to have a Strength 14 and fight with a battleaxe, you can still be an effective character. You won't be as good as a fighter with a higher Strength, but those little +s aren't as critical for success in this edition. But--paradoxically sounding--they are also a bigger deal because there are fewer places you can get them, and they cap out at lower numbers.
The jury is still out on whether it would be as/more difficult in other editions; so far I see more modifications that would have to be made to 5E than with 2E. It's just a question of whether what remains after those modifications makes the effort worthwhile. The purpose in the theorizing is an attempt to evaluate the extent of that effort.
2e is my favorite D&D "feel." 5e is my favorite rule set, because it does a better job of enabling me to play with that feel than other editions, while cleaning up a lot of the mechanical issues of 2e I didn't like. So let's see if I can give you some useful ideas to consider.
The ones that are standing out to me as major considerations are bard, paladin, and ranger. If you don't want highly magical bards, your best bet is probably just to ignore that class and make a new rogue subclass to represent the bard you want--probably selecting abilities for him from the bard's non-magical abilities--which would probably be fairly easy. I kind of want to see how fast and well I can do that now just as an exercise, despite the fact that I have no intention of using the results. That link I gave above (with the non-magical ranger) gives advice on how to modify classes and subclasses. The non-magical ranger is an option if you like it, and paladin is really supposed to be a holy warrior anyway. Otherwise he's a fighter. You might allow a higher-level fighter to take the Magic Initiate (cleric) feat if you wanted to replicate a paladin with just a touch of magic (or Magic Initiate (druid) for a ranger).
One of the lead designers has gestalt multiclassing (which we presume is referring to AD&D style demi-human multiclassing) on his list of subjects to give us free rules for in the future. It was one of a number of things that was going to be in the DMG (and apparently already had rules created for) but got cut in the final pass due to space considerations. I'm really looking forward to that one--as it's important for my own campaign.
Cantrips. Just give full-casters some 0th-level spell slots and let them automatically prepare/know the number of cantrips listed. They can prepare more with their other spell preparations.
As far as cleric domains...I'm personally a fan of the relatively small number of domains. What you have to realize is that they are supposed to be both broad and significant. The pantheons at the back of the DMG give you examples of which domains work well for which deities. If you read the intro paragraphs for each domain you will see how they are supposed to be more or less comprehensive. Knowledge includes (amongst other things) magic and crafting for instance, and is appropriate for the dwarf god Moradin. Trickery covers fortune and luck sorts of concepts, as well as darkness, along with other tricksy things. Light hits beauty, and truth, as well as fire. For your elements in general, you could use Nature for any or all, and Tempest can give you water, air, cold, Zeus, Thor and more. The other domains are similar--and even the ones I listed have more example uses. The Death domain in the DMG is broad enough to be appropriate for many stripes of evil, and it also works as a non-evil domain for gods of the dead like Kelemvor. It isn't set up with the same level of fine granularity that 3e had, where they would just make a new domain whenever they wanted. Instead, the domains cover everything with a little bit of thought. And they give you
substantial stuff. Clerics of two different domains can almost look like completely different classes. It's more along the lines of 2e specialty priests than 3e domains.
One thing you might want to take into account when determining the ease of modification is that feats are
big. You can really stick a lot into a feat. In conversion terms, each one of them is about equal to about three feats in 3e (or two epic feats), and sometimes they are even better than that because of the way the rules work. There are no feat-chains needed. A feat is supposed to give you everything you need to specialize in a particular thing. This means you can add almost anything you want to add to character capabilities via a feat. If you decide that you want it to take up two feats, then you can
really add a lot. Two feats is a poor man's wizard (Magic Initiate + Ritual Caster), or any variety of powerful combat combinations.
What other sorts of modifications do you feel are necessary to get what you're going for?
I guess I'm a harder sell. I'm definitely still considering it, and as I said, I've got more to learn before making a decision. I've seen enough that I really want to like 5E, but at the same time I see a lot of problems that would come from using it as well. There are definitely a lot of problems from previous editions which it solves nicely. 5E does appear to be a good system, I'm just uncertain whether it is the right system for what I'm trying to do.
Ah yes...I know that feeling well.