384
When it all comes down to a single roll.
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I guess if you throw an egregious amount of magical power at a problem it DOES solve it!
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.
You don't need to because bounded accuracy doesn't need to exist, often it's actively detrimental. See the common houserule that some checks can't be attempted without proficiency.