why not battlemaster on a caster?
because casters already have a laundry list of options that provide versatility or allow them to influence things and martials have pretty much diddly squat? like, let's just look at what offensive cantrips ALONE provide shall we? i'll skip over the fact that most if not all of them deal some form of energy damage, quite a few have range and in general can target a range of saves amongst themselves as an alternative to attack rolls.
Acid splash - multitarget
Booming blade - movement control
Chill touch - healing control, applies attack roll disadvantage to certain foes
Create bonfire - persistant hazard creation
Eldritch Blast - N/A (although invocations can give a range of additional effects)
Firebolt - N/A (can ignite flammable objects but i'd label that as ribbon ability)
Frostbite - defensive control
Green flame blade - autohit damage to secondary target
Infestation - forced (if uncontroled) movement
Lightning lure - forced movement
Mind sliver - weakens saves
Poison spray - N/A
Primal savagery - N/A
Produce flame - N/A
Ray of frost - movement control
Sacred flame - ignores cover
Sapping sting - inflict condition (prone)
Shocking grasp - action economy control, advantage against certain targets
Sword burst - AoE
Thorn whip - forced movement
Thunderclap - AoE
Toll the dead - conditional extra damage
Vicious mockery - attack roll disadvantage
Word of radiance - AoE
that's four cantrips, five if you stretch to include eldritch blast which can gain riders, that purely do straight basic damage to single target without any form of additional bonus or somesuch in a single action out of
twenty-four cantrips, not to mention the pages upon pages of leveled spells that are bigger and badder than these, that's why martials deserve battlemaster and casters don't.