Ok. I have no problem with that. I get that...
I think what might have my "internal consistency" hackles up is the idea that it would be perfectly fine and seem "normal" for an "Arcane Dabbler" to gain access to things like
Fireball or
Cloudkill...or the list of spells RW listed. Earthquake?
Meteor Swarm?!
"Yeah but it's only once a day."
No. That's not "ok." The wizards/mages/even sorcerers study/research/or even with an innate talent work for years to gain mastery over their magical powers. Some guy who's become a Fighter Lord, in passing, just happens to pick up a little magic...which includes how to work a 3rd or 4th or higher level/tiered spell?!
Ow. There's that "makes sense" hackle getting all knotted again.
I have no problem with an "Arcane Dabbler" feat/theme/specialty/what have you...or a "Nature's Adept" for just basic druidic spell use (clerical gets a little tougher to justify)...a "Sneak" for some limited Stealth or Open Locks...or a "Soldier/Watchman" for a basic level of weapon proficiency (a wizard who can effectively wield a sword, for the classic example). I'm all for it. Makes sense, good flavor, opens up all kinds of avenues for character concepts. Full of win.
But all of these things are BASIC/STARTER/1st level type ability. A Cleric from a rural/farming background who learns from a local druid or just has some affinity with the local nature spirits or however you want to fluff it can: Pass without Trace (as a mundane ability) and cast Faerie Fire or Entangle 1/day. Totally works. A Thief who takes "Scout" for some tracking, maybe some herbalism and/or nature-survival skills to be a kinda "Ranger-lite." Totally works.
A 19th level fighter who's learned, through their DABBLING, how to cast Magic Missle or Sleep? No problem. Heck, I'll even go to, eventually, 2nd level/tier spells. Web? See Invisiblity? Mirror Image? Levitate? Fine. Fireball/Cloudkill/Meteor Swarm? Nuh-no. It takes many levels for the FULL caster class
whose primary function is to work with magic to get to those. Stuff over 1st or 2nd tiered magic/spells should be wellll beyond the Dabbler's capacity.
To borrow from a couple of other posts that closely mirror my tastes:
1) When you take the feat/specialty/whatever...at
any level, you get access to, let's even say a choice of 3 (woohoo!) cantrips.
2) Whenever you get to take it again/put in another rank or however this would work: get a 1st level spell 1/day.
3) Next time: 2 1st level spells/day...and, how 'bout, you can use wands and divinatory magic items normally reserved for wizards/sorcerers. (Want crystal ball using rangers? Have a field day!

)
4) 2 1st and 1 2nd tier spell...and can use any magic items reserved for wizards/sorcerers.
That's it! That's the extent a "dabbler" can fathom/master the mysteries of the Arcane.
Beyond that/for more power you need to full on multi-class. I am totally with you in mbeing against class-dipping. 3e-style multi-classing is/was a travesty to me.
So, all this long-windedness is really just saying, I like and support the idea of having these "lite dipping" type specialties/feats/skill packages/however they're going to be presented. But what that gives you, by no means, should be dependent on what level you are when you take them, nor should they give more than a few simple basic beginner-type abilities. Since that what they are. Having a little extra knowledge of stuff outside your class.
If you are a 19th level fighter who wants to cast Fireball...then your next "level up", take your starting level 1 in Mage and get to level 5. Probably, at that level, just easier to commission a wizard to make you (or go questing for) a 1/day Fireball-ring or something like that.
--SD