Crimson Longinus
Legend
I was talking about OP's suggestion which effectively bans combat spells. No one will do nothing for four rounds in order to cast a magic missile.I'm not banning combat spells. Fireball, magic missile and many others exist would still exist. It is just that cantrips are banned.
There is no need to grant a spell caster more martial options as they are already quite powerful outside of combat. Although I would consider allowing a spell caster to pick up additional weapon proficiencies and maybe wear armor at some other penalty (maybe a penalty to concentration saves if they wear armor).
Balance is maintained in the general scope of the game as a whole, it is just that balance in combat is driven in favor of non-spellcasting classes and, in this situation, that is a desirable outcome.
Although this also brings up all the classes and subclasses that are overtly magical that aren't casters.... (a lot of the later barbarian subclasses for example). I'd probably just ban those out-right. Ban warlocks and sorcerers and limit wizards as defined.
But yes, if you want less video gamey magic pew pew (I can sympathise with that, it does feel out of place in some settings) then indeed removing combat cantrips (and leaving other combat spells to function normally) but giving casters more weapon and possibly armour profiencies to compensate could work OKish. Now some players might not like the resulting flavour, but that's another matter. Warlocks however would be boned without eldritch blast, except if they were hexbaldes.