That would just make caster strictly better than martials at low levels.
No it wouldn't. If you are doing point buy it would be generally worse damage until tier 3. They would be generally behind at 1st level, further behind at 5th level when martials get a 3rd attack and still generally behind at 11th level.
For example level 1 with a 16 attack stat:
Ranged Attack:
2 attacks with a longbow: 2d8+6 = 15 damage
1 attack with a Heavy crossbow and THE BEST ranged cantrip against an already damaged enemy: 1d10+3+1d12 = 15 damage (the cantrip is a save which will hit less and has a much shorter range)
1 attack with a Heavy crossbow and the BEST ranged attack cantrip: 1d10+3+1d10 = 14 damage
Melee attacks:
2 attacks with a greatsword 4d6+6=20 damage
1 attack with a greatsword and 1 Blade cantrip 4d6+6=20 damage plus possible secondary damage
Reach/Ranged Melee Attacks
2 attacks with a Glaive 2d10+6=17 damage
1 attack with a Glaive and 1 Thorn Whip 1d10+3+1d6 = 12 damage
Two-Weapon Fighting
3 attacks with a shortsword = 3d6+6 = 16.5
2 attacks with a shortsword and a blade cantrip with a shortsword 3d6+6 = 17.5 damage plus possible secondary damage.
These numbers assume no fighting style and do not consider splitting your abilities between a casting stat and a weapon stat. All of these things serve to improve the weapon damage more than the cantrip damage.
If you look at these examples they pull from the best available cantrips and combine that with the best available weapons. While this is doable at first level it is not exactly easy. For example a Hexblade or Cleric with the right subclass could go heavy crossbow and toll the dead, but a base cleric couldn't and no Wizard or Sorcerer could without getting the crossbow proficency through a race. Likewise only a Hexblade could go with a Greatsword, Glaive or 2 shortswords and a blade cantrip at first level. If you put caster-appropriate weapons in there the numbers are a lot worse for using a cantrip and an attack at 1st level.