The discussion right now shouldn't be whether attack cantrips should be removed from the game... but rather should the DMG include a fully-playtested module that removes cantrips or moves them to each classes 1st level spell list, and what has to occur or get added to make that balanced.
That is indeed an interesting question. I was just pondering that. Ideally, the module would make it possible for a cantrippy wizard and a non-cantrippy wizard to play side by side.
Let's see what the overall benefit is, by level, of using
ray of frost versus a crossbow. (Warning: Lots of educated guesswork ahead.) We'll discount the slow effect, which in my experience has very limited usefulness, and just look at damage. Assume you start with Int 17/Dex 12, and put your first two stat bumps into boosting Int. Also assume that your typical target has an AC of 13, which is about what the typical humanoid mook has. We'll bump that value by 1 for every 5 levels to reflect generally tougher opposition (so AC 14 at level 5, AC 15 at level 10, etc.).
Level 1:
Ray of frost hits on 9 (60% chance) for 1d8 damage (4.5). Average DPR: 2.70
Crossbow hits on 11 (50% chance) for 1d8+1 damage (5.5). Average DPR: 2.75
Value of cantrip over crossbow: None whatsoever
Level 5:
Ray of frost hits on 8 (65% chance) for 2d8 damage (9). Average DPR: 5.85
Crossbow hits on 11 (50% chance) for 1d8+1 damage (5.5). Average DPR: 2.75
Value of cantrip over crossbow: 3.1 per round
Level 10:
Ray of frost hits on 7 (70% chance) for 3d8 damage (13.5). Average DPR: 9.45
Crossbow hits on 11 (50% chance) for 1d8+1 damage (5.5). Average DPR: 2.75
Value of cantrip over crossbow: 6.7 per round
Level 15:
Ray of frost hits on 6 (75% chance) for 4d8 damage (18). Average DPR: 13.5
Crossbow hits on 10 (55% chance) for 1d8+1 damage (5.5). Average DPR: 3.025
Value of cantrip over crossbow: 10.475 per round
(I'm not bothering with level 20. By that point you have Spell Mastery and the question of cantrips is moot.)
So, that gives us a baseline--but of course the benefit only applies in rounds in which you don't cast a "real" spell. Let's assume the typical adventuring day includes 20 combat rounds (say, four encounters of five rounds apiece). Assume also that you will burn through 3/4 of your spell slots, rounded down, during said adventuring day, holding the rest in reserve in case of emergency. So a 1st-level wizard will cast 19 cantrips per day; a 5th-level wizard will cast 14; a 10th-level wizard will cast 9; and a 15th-level wizard will cast 7.
Very roughly, then, how many bonus 1st-level spells does a wizard need in order to make up for the loss of attack cantrips? Conveniently, we have a handy metric for 1st-level spell damage--
magic missile, which does a flat 13.5 regardless of level. So, let's give the non-cantrip wizard some number of bonus 1st-level slots, such that casting that many
magic missiles and then falling back on a crossbow deals equivalent damage to casting
ray of frost the whole time.
Level 1: No bonus spells needed.
Level 5: 4 bonus
magic missiles needed.
Level 10: 5.6 bonus
magic missiles needed.
Level 15: 7 bonus
magic missiles needed.
Of course, there is an awful lot of guesswork and estimation in these results. They would need heavy playtesting to make sure the estimates hold up. But I think it's good enough to give a rough idea of what such a module would look like. If I were going to try a quick-and-dirty home fix, I would probably say 1 bonus 1st-level slot, plus 1 for every two wizard levels.