Well so far - the players just reached 5th level - the players have had to make a couple poison saves against giant spiders, some STR saves against being knocked prone (dire wolves), one disease save (gas spore), and a series of paralysis saves (carrion crawler). They have fought one caster enemy, a deathlock, so a few had to save against hunger of hadar for 2d6 damage. On the other hand, two of the five PCs use cantrips with saves as their primary attack. So right now we're looking at maybe 20-30 player saves across the whole campaign, vs. something like 8ish saves for monsters every encounter. They have enjoyed the occasional "auto-12" on toll the dead when the monster Nat 1s.
Although, as I type this, I realize that the reason this works at my table is probably based a second house rule! We did away with Inspiration (actually, revamped it to be very story- and player-based, and no one has triggered it yet), and replaced it with Luck Points. Generally you get 1 per session (our sessions are generally 3-4 hours), and you can "store" up to 3. [There's more to it than that.] You can spend a Luck Point to reroll "after seeing the die, before knowing the result", or you can spend a Luck Point to change a "missed by 1" to a success, or "made it exactly" to a failure. So when a PC rolls a Nat 1 on a save (or suffers a Critical Hit), they spend a Luck Point...