I played many years of several editions of the game that did not have cantrips, and they add two huge steps forward that would need to be implemented in other ways in order for me to want to play without them.
1. They made magical characters feel magical.
There's a school of D&D Dogma in which they did the opposite, though: that at-will magic becomes commonplace, and therefore mundane. (TBH, by that logic, reliable n/day magic has the same issue on a world-building level.)
However, you could add back the minor utility of cantrips with a long-duration low-level convenience-magic spell - as 2e did.
2. They made casters useful when they weren't using slots. They brought down the average power of the slots to keep them balanced. These are closely related.
They are, and they didn't actually happen that way, IMHO. 3e brought up the baseline effectiveness of casters by giving the light crossbow - a safe-to-use, OK attack for rounds that didn't warrant casting. It in no way brought down the effectiveness of spells, giving casters moar spells, loosening restrictions on spells, like making DCs and Concentration checks subject to heavy optimization, making casting in armor possible with some build work, evading AoOs with a check, etc, etc...
4e actually did bring up the baseline of 'casters' (other than Martial Sources) and bring down their daily resources to balance - they also gave the non-casters the same balance scheme.
Relative to 3e, 5e brought up the baseline of casters dramatically, and pulled in the power of slots a bit (not always consistently). Relative to 4e, 5e pulled in the at-will baseline for casters slightly, and greatly expanded the number & power of slots, while buffing up the martial base-line DPR with Extra Attack and eliminating limited resources for them almost completely.
So, really, if balance is a concern, eliminating cantrips entirely won't hurt a bit. It won't be
enough either, and it's the kind of swingy, take-turns-not-having-fun 'balance' we had in the classic game, but it certainly not going to leave casters in the cold.
3. Keep different classes different. In other words, if every class is a fighter, you only need one class. Don't make all the classes feel the same.
Also not much of a concern. The classes that have cantrips are already very different from those who do not - and already not very different from eachother, with that difference mostly being in a handful of unique spells, and the odd class ability.