This is not a good way to solve the problem you're trying to solve.
What you're effectively moving towards is a "fun tax." You're balancing X% of gameplay at an overpowered level against Y% of effective non-participation in gameplay. Game designers talk about this from time to time, and the outcome is almost always negative.
My problem is not just the cantrips, but the fact that spellcasters have super-powerful spells that make them superior to some classes. In all other versions of D&D that I have played, they were "balanced" by the fact that once they have used up all their spells, they're not as effective (I said "balanced" because they are almost all Tier 1/2 in other editions). But now, they can cast super-powerful spells and still be at least not useless after using all their spells. (So they were the better classes before 5e, and became even better than before in 5e.)
For now, let's assume your balance assertions are right: Wizards have a powerful arsenal of spells that unbalances them, and you are trying to fix that.
I'm also excluding warlocks from this discussion. Warlocks are a special case in that their cantrip is much better than average, and their non-cantrip spellcasting is severely limited. If your issue is with warlocks, that is a different issue.
Resting is primarily in the hands of the player characters, and allows them to reset their casters' spells. Given the choice between taking a rest or being useless, most players will choose to take the rest.
The 15-minute adventuring day is already a known problem, and this fix would make it worse. You're giving players much more incentive to follow this immersion killing pattern.
There are solutions to the 15-minute adventuring day. Ways to put pressure on the party. But these ultimately all involve taking a choice away from the player characters. Less choice is bad, and forcing the DM to build every scenario with high time pressure is awkward.
Even with rests out of the equation, the players still get to choose when they are overpowered and when they are underpowered. The most common result of this is a "nova" mentality... Go all out on the important fights, and hold back on the "trash."
This means that on the fights you care about, the wizard is still overpowered. You're trying to compensate for this by underpowering the wizard on the fights that don't matter. This still leaves you with a fundamental problem: When it matters, the wizard is overpowered.
Cantrips Aren't That Great
This is why your "fix" isn't the end of the world (except for warlocks), and why you still have full casters on your table.
At fifth level, a dueling fighter gets two attacks at 1d8 + 5. This is much better than a wizard's single attack at 2d10 + 0.
A rogue at that same level can easily get 4d6 + 3. Which is, again, clearly better.
Making a class's weakest attack weaker isn't going to undo phenomenal cosmic power.
If Something is Broken, Fix That
If you feel that full casters are overpowered, then you should fix the overpowered abilities. "Fixing" weak abilities to make the class less fun is just passive aggressive.
If the problem is that the wizard can tear a hole to another dimension, or that they can sweep a room clear of goblins in a fiery conflagration, then lowering their damage output by 10% on the fights that don't matter isn't going to change things. They can still do the broken stuff just as often as they did before.
Is It Really Broken?
My general experience is that casters are good, but not good to the exclusion of all other classes. This is backed up by analysis on overall damage output and cantrips specifically which shows that there is much greater parity in this edition.
While full casters still get access to abilities that mundane classes can't replicate (teleportation across large distances, or creating doors from nothing) the gap in day-to-day adventuring has narrowed.
There are a few reasons for this:
The Concentration mechanic drastically limits a full caster's options. Many effective, non-damage spells require concentration, making them mutually exclusive.
A large emphasis has been placed on giving the other classes utility and special abilities beyond "I hit it with a basic attack."
The overall curve of damage has been flattened.
The purpose of cantrips isn't to make full casters unstoppable engines of arcane destruction. The purpose of cantrips is that a wizard can do "wizard stuff" for the whole adventure. You don't have this awkward transition where you're Gandalf in one scene, and a crossbowman in the next.
Nerfing a flavor ability like this isn't going to solve larger balance problems.