TL;DR = I voted for a "Long Rest Limit".
I thought about this in another thread where combat cantrips were discussed.
I absolutely don't want to see mages going back to carrying darts and crossbows. Given that D&D does not have a "magic is exhausting" mechanic built-in (which is essentially what some of the "keep rolling until you fail" suggestions from other systems lead to), my friends and I decided on a "solution" that might also apply to the OP's question as well:
You get four times your spellcasting bonus (minimum +1), plus your proficiency bonus, cantrips per day (Long Rest). This provides an expected bottom of 14 casts for the 1st level 16stat caster, to 26 for the 17th level 20stat caster. [Or, for the no-math'ers, give them 20 cantrips, period, no math, no progression. also, easily trackable on a d20!] Maybe complicate a little for partial- and multi-class casters.
Lots and plenty. But it is still a limit. You can't spam guidance or minor image (for concealment, like the AT in my game does), and still expect to throw out firebolts every round. My sorcerer tossed mind sliver and Quickened spells all the time (until he ran out of sorcery points and slots); with this rule, maybe not so much.
(Another option we explored was "combat cantrips never get better". so the mage never has to carry a dart or crossbow, he always has that d8 or d10 magical attack... but he really ought to be using his levelled spells!)
Otherwise, leaving combat cantrips out of the conversation... I like progression. So a simple "spellcasting stat" or "PB" foundation for a limit that can grow is at least better than a flat "5". (for example, I would lean into "Stat + PB", so you get a range of 5 to 11 over time). I also like tying it to "caster level", as that better adjusts for hybrid casters and multiclassing (I hate the fighter 16 / wizard 1 throwing 4d10 firebolts!), but since the baseline there is "1 to 20" for the pure caster, it's much harder to define in a way that is useful to the pure caster and elegant for the hybrid. and then there's the multi-caster multiclasser! Ooof! Our thought experiments down this line ended up with "4 castings per day, plus stat bonus; plus 1 for each spell slot LEVEL beyond the 1st". So the starting mage has 7 castings, and the 17th level mage has 17.