What do people think? Is there any issue or balance concern that I haven't considered with this mechanic? Any foreseeable problems to be prepared for? Has anyone ever tried this?
I see this as highly problematic on two fronts.
First, you are essentially giving the wizard free extra prepared spells. While two extra first level options aren't that big a deal, six extra options of any level most certainly could be. Instead of having to carefully choose your spells- something that I think is a meaningful choice for casters who prepare spells- you have added flexibility sufficient to make that choice significantly less meaningful. Sure, this comes at the cost of no cantrips, but a smart wizard focused on optimal combat could simply always prep
fire bolt as his only cantrip and save those other prepared spells for a handful of additional utility. Why choose between fireball and fly when you have enough spell slots to do both without missing out on anything else?
The second issue is with a wizard who doesn't pack any cantrips. Once out of slots, he's basically like a 1e magic-user, reduced to throwing daggers or shooting a crossbow. Taking cantrips away (or rather, giving the option to go cantrip-less) means that the wizard runs out of spell slots earlier (because even the least challenge requiring magic requires a spell slot), and that means that he is not able to contribute to the same degree in later encounters. He isn't dealing his expected damage round after round; he's all alpha strike all the time followed by a big bag of suck.
Now, the counter to this argument is, "Well, then, prepare a cantrip or two." Which is fine-
if every wizard uses that option. But the option to not do so is a trap. And trap options sucks. That's why they pretty much eliminated them from 5e. There's no "take a feat to gain 3 hps" in 5e. That's a design choice that I think this option undermines; it allows a pc to intentionally or inadvertently set himself up to suck. Sure, it's possible for a wizard to choose terrible spells and cantrips in the base 5e rules, but you'd really have to set out to do it.
So yeah. Not to my taste, though I understand the intention. What if, instead, you just let wizards scribe more cantrips into their books and prepare the standard number separate from their leveled spells?