Yeah, it's a bit of a conundrum.[...]
In 5e, that balance is upended because of that prior thought. What should a fighter be, other than a character who is superior at fighting (it's almost a truism)? And yet, it would seem that spellcasters should have:
A. The ability to use cantrips every round that gives them roughly the equivalent of the martial character's attacks; and
B. The ability to use combat spells that aren't cantrips- from damage, to control, to buffs, to whatever, because that gives them variety in combat ... you know, meaningful choice; and
C. The ability to have numerous out-of-combat spells because spellcasting isn't just about combat, man, and that's what they have cantrips for anyway; and
D. The ability to use their numerous spells to affect the game in all of the pillars in a supernatural way, because ...
Which I totally understand. I, too, want my characters to be the awesome-est at everything! And yet, if spellcasters are required to be just as good as the martial characters at, um, martial stuff (combat), and spellcasters also get all the other goodies that spellcasters will get outside of combat, and if martials don't have that ... then, that kind of sucks for the martial, doesn't it?
And you're left with either giving martial spells (spell inflation), or not.
And maybe I'm missing something on this, but the specific thoughts (that spellcasters had to be just as good as martials at combat) surprised me somewhat. Is it because everyone is playing 5e as a tactical combat game (I didn't think so)?
To feel awesome, fighter-types need to be awesome at fighting, and, to feel awesome, magic-types need to feel awesome at magic.
BUT magic is a bigger tent than fighting. And, really, the big tent that is magic contains the small tent that is fighting... So you can't really feel awesome at magic if you are heinously suckass at fighting.
AND if everyone is awesome at fighting, but magic-types are awesome at other things, magic-types are just better.
There aren't any great fixes to this that make intuitive sense. You get pushback like "how can a warlord shout somebody's arm back on?" if you give fighter-types the ability to do things too far outside the fighting tent, and you undermine their fighter-type-ness if you give them spells.
Tentatively, I think the best way out of this is for fighter-types to get better magic items than magic-types do, which also allow them to do things that are normally in the magic tent. For example: that +1 greatsword for the barbarian might also detect lies and provide an at will 30' jump--now the barbarian is good at the social and exploration pillars--where, by comparison, the wizard just gets a +1 wand of meh, or a headband of 'doing that thing which wizards do already but now slightly more of it'. Obviously, this is something that needs a conscientious DM to make it work correctly (and/or publications that are written by someone with sense). Maybe magic items could, in general, offer more versatility than power, since magic-types have versatility for days and fighter-types do not.