4th is bloated. I like 5E's spells and class structure better. I like the 12-14 core classes of 5E over the dozens of classes of 4th. The amount of work to bring what I like of 5th into 4th is a lot smaller than what it would take to bring what I like of 5th into 4th (combining classes, consolidating powers ...).
I would advise stating this up front. Not doing so risks people thinking you're not being honest and that you're engaging in edition wars via "collaborative debate".....namely "I want to change this because I see it as a problem, lets discuss" when underneath you really want to say 4e is better, lets remake 4e. In this instance, this is literally your intention for melee attacks and cantrips. That's completely fine, but trying to argue there's something "wrong" with 5e, when in fact all you want to do is bring in some function of 4e you like without breaking 5e, is going to start edition wars. When that happens, no one wins.
Cantrip attackers often get an ability bonus rider, and other nifty things (evoked gets +Int and damage on a save, Warlock gets +cha to each ray). Since most classes other than the Fighter, monk, and beast master Ranger are only making 2 attacks tops, I don't think the feel would change that much. The gains in better opportunity attacks and better multiclass progression are a good trade to me.
Using two examples which require specific cognitive choice (selecting a subclass for the Evoker, and not only selecting Eldrich blast as a cantrip, but then also choosing a specific invocation), is not justification enough for rewriting entirely how 4 core martial classes, plus War Cleric and Valour bard, deal with their 2nd attacks.
What is a perfectly reasonable justification is "I really liked the at-will power system for 4e and how it worked across all classes, and I want to replicate that in 5e to replace all main hand melee attacks". There's no value judgement, you can attach the rider "I think my players will prefer it" or "I want to do it for myself because it's fun/interesting", and most importantly you're not saying your way is "Better" (which by inference says another persons view is "wrong"). Your first post pretty much said that - and that's all the justification you need.
By defending you preference mechanically, you diminish your argument that "I want to do this, and I don't think everyone should do it".
The casters in my games seem to use their cantrips a lot. The EK rushed to get the feat that lets you use a cantrip as an opportunity Attack even.
That's fine (that's kinda what EKs do and a feat is designed in 5e to be heavy tax, hence why fighters get them because that's what fighters do) - though I would take pains to check with your martial class players (or players who might want to play martial characters in the future) they're ok with this, and understand the ramifications. I can foresee a lot of players who would be upset that they don't get a 2nd chance to hit on their turn after rolling a 1, or that they just feel like spell casters (i.e. 4th Ed's issue with "Fighter Casts Punch")
You may well have done this and they're all happy with it - just checking.
I don't think WotC did a bad job. I do think they fixed spellcaster multiclassing in 5th but somehow "broke" warrior multiclassing, when it was the other way around in 3E. By adding damage scaling to weapon attacks, the progression for even 1/1 multiclassers would be a lot more smooth, and players wouldn't have to rush to 5th level quite as fast if their character idea really warranted lower level multiclassing (I know I'm itching to play a Rogue 3/Paladin X inspired by the 3 Musketeers next time I get a chance to play).
Again - just try and keep a lid on the edition warring - you're insulting people like myself and probably that vast majority of players who don't feel warrior multiclassing is somehow "Broken".....what you are implying is that somehow we are stupid or mistaken when we quite like the way 5e has limited and streamlined multiclassing to make it much more focused, rather than the minmaxers wet dream 3.5e and pathfinder is. It's clearly not "Broken" as you say - it might not be to your taste (which is totally fine BTW), but it's not even remotely broken. There's a difference between a design CHOICE and a design OVERSIGHT. You want low-level multiclassing to be a penalty free, that's fine. WotC CHOSE to do things another way and plenty of people are happy about that.
Basically, saying "It's not fair that I have to take 5 levels of my initial martial class before I can multiclass otherwise I don't get an extra attack. It's stupid!" is the argument of a child. Saying "I would really like to design a way to multiclass martial characters that treats extra attack as something more similar to 3.5e BAB" is pretty hard to argue with. I *want* to do something, and my players are ok with it is bullet proof (very much like the argument "I really want to have Chicken Cassoulet tonight")
So right now, personally, my advice would be to rewrite the initial post and be as transparent as possible about what you are trying to do (namely create D&D 4.8 with mostly 5e but with 4e at-will power cards), and what you want from posters (it seems mostly you want validation - I'd say your players are going to be better placed to supply that than an internet forum). That way, you're more likely to get the feedback you want, less likely to have people (like me) pointing out that 5e is deliberately made this way (as you've said, you know and accept this), and people will be more likely to help you identify potential areas of design oversight (while detractors have less space into which to insert an edition war disguised as something else)
For instance - Does magic item additional damage scale with weapon damage? Barbarians now do 50% more damage with a 2[W] attack on average with a 50/50 chance to hit (2d12+STR+Rage, half on a miss) factoring in the +1 - was this intentional?
Personally, I like 4e and 5e just as much as each other, for differing reasons, and don't see the burning need to try and combine the two. If you want to, go for it, I just think you'll get a bit mroe traction and engagement if you are a little more up front about it.....