D&D 5E Limiting cantrips - advice needed

[Gadget]

I'm still not 100% sure yet, but I'll start with something along the lines of 5 casts per short rest, and go from there.

One of my players did some math work, and he arrived at the following conclusions:
1. given that we usually have 5 to 7 encounters a day, lasting usually between 3-4 rounds each, there's usually between 20-25 rounds of combat in a typical dungeon day.
2. At level 5 (almost the level we're in), a Wiz/Sorc/Bard/etc. will have around 9 slots of 1st level and higher, not counting arcane recovery. At level 10, it's 15 slots, and at 15th level, 17 slots.
3. Considering most os these slots will be spent in combat (again, not counting arcane recovery and similiar abilities), that leaves around 10-15 rounds where the caster will most likely need to use cantrips or the like.
4. 5/short rest will ensure that, considering 1-2 short rests a day, the caster will have cantrips available for combat for the most part, but at the same time, will have to manage the resource and cantrips would not be prone to abuse.

cheers!

Is this 5 per cantrip, or 5 total per short rest. I would think that the later would tend to eliminate the use of utility cantrips, as one would be tempted to reserve these slots 'just in case'.

 

[Mouseferatu]

I didn't say a caster should be able to fire cantrips for exactly as long as someone can swing an axe. Or longer. Or shorter.

I suppose I shouldn't have used examples, since people are reading into them. So, my bare-bones, basic point:

It is reasonable to establish common sense limits to activities that will eventually tire someone out, even where the mechanics of the game do not. There is no reason for spellcasting to be an exception to this.

Period. Full stop. My entire point.

And I don't even consider this houseruling, any more than it's a house rule to say "You can't fly by rolling an Acrobatics check every round to keep dodging the ground." As always, no "badwrongfun," play how you want. But for me and for the DMs I know, someone complaining about a DM enforcing such a basic level of common sense? Wouldn't be welcome at the table very long.