Honestly even without the dice buffs, it's pretty easy to break - Expertise is another big culprit. At T4, with regular proficiency, you can get up to a +11 modifier without magic items or spells, meaning your average is going to hover in the ~20s, ~25s if you can get advantage, but the range is still bounded from 12-31, only a 10% chance of achieving the 'nearly impossible' for a character representing the pinnacle of ability and adventuring prowess. Makes sense.
With expertise, the modifier goes up to +17, average roll 27, 32 with advantage, range of 18-37, which gives a 40% chance of achieving 'nearly impossible' DCs. Makes less sense. If you happen to be playing a rogue with expertise in Thieves tools and sleight of hand, and wearing gloves of thievery, your skill floor is 32(!!!) - You literally cannot fail to pick a lock or a pocket unless the DM creates a scenario that breaks bounded accuracy. And then, of course, you can throw BI, guidance, etc. etc. on top of that...
If I had to homebrew a quick fix, I'd suggest something along the lines of "When making an attack, check, or saving throw while under the effects of a spell or feature that allows you to add additional dice to the d20 roll, such as Bardic Inspiration, you may only gain the benefit from one feature on a single roll. If multiple features would add dice, you may choose which feature to add the dice from when you roll."
Totally ranting at this point - I think 5e's got good bones but there's a lot of problems inherent with simplifying down to a single scaling number. Saving throws swing the opposite way - depending on the creature you're facing, it can be literally impossible for a PC and/or NPC to make a saving throw against DC 20 and up if you don't have proficiency, and by design you won't have proficiency approximately 2/3 of the time (this is also why named monsters get legendary saves in 5e.) Not saying we need to go back to 3.5/PF with like a dozen different sources for bonuses, definitely not that, but proficiency needs to be less binary for a more balanced and playable game, especially at higher tiers.