Apologies - I am still stuck up with Bounded Accuracy and Expertise. As far as I understand from the answers about what it means to break bounded accuracy, from the related Q&As about how bonuses to attack and skills scale, and what the design objectives for this were, a core idea of bounded accuracy is to keep challenges relevant and interesting throughout the PCs career:
Goblins remain a threat, even at higher levels, you do not need to change their stats
You do not need to scale DCs. A hard skill challenge remains hard, even at higher levels.
It avoids impossible tasks and automatic successes, so rolling the dice remains meaningful
It allows everyone to participate. The wizard may not deal quite as much damage as the fighter when resorting to their crossbow or cantrip, but they still matter and can meaningfully contribute. The fighter may not have as high a perception as the ranger, but they still have a chance.
This is achieved by the rather flat increase of the bonuses for both skill checks and attacks over the PC's career: barring magic items, they can be expected to increase only by 6 points, from +5 at level one, to +11 at level 20.
For combat, this seems to work pretty well. On the chart below, the blue line is the average result on an attack or check for a proficient character with a maximized ability score, and the black line is the expected AC of monsters as given in the monster building rules in the DMG (p. 274). You can see how the ratio remains about even for all levels, with the expected to hit about 2-3 points higher, resuling in an about 65% hit chance throughout. Instead of changing the hit chance, the game scales the hit points and damage, so a single hit from a mighty hero will kill a weaker monster. This works (mostly, PCs can find ways to build characters with very high ACs).
For unopposed skill checks, the DCs are entirely static. Hard is hard is hard. The DMG disusses the matter as follows (page 238):
If the only DCs you ever use are 10, 15, and 20, your game will run just fine. Keep in mind that a character with a 10 in the associated ability and no proficiency will succeed at an easy task around 50 percent of the time. A moderate task requires a higher score or proficiency for success, whereas a hard task typically requires both. A big dose of luck with the d20 also doesn't hurt.
If you find yourself thinking, "This task is especially hard," you can use a higher DC, but do so with caution and consider the level of the characters. A DC 25 task is very hard for low-level characters to accomplish, but it becomes more reasonable after 10th level or so. A DC 30 check is nearly impossible for most low-level characters. A 20th-level character with proficiency and a relevant ability score of 20 still needs a 19 or 20 on the die roll to succeed at a task of this difficulty.
You can see from the yellow graphs for Good Stat or Proficient (average stat), that the DMG is right on this. These characters will have about a coin toss of a chance throughout their career with an moderate task ("medium" in the chart), a bit less early on, a bit more later on.
Proficient characters with good abilitiy scores will outgrow moderate over the course of their career, and be a match for hard challenges towards the end. One can expect that mighty heroes will confront more powerful enemies, with likewise better skills, so opposed checks might still scale. And these opponents may afford better traps or secret doors, so their lairs may sport hard challenges where normal dungeons had medium ones after about level 10, as the DMG suggests. That shift pretty much equalizes progress, and keep things interesting. So far, so good.
What I do not understand is how Expertise fits with this (shown as the red line in the graph). In particular in combination with Reliable Talent for rogues, a minium result of 22 or so after level 11 is guaranteeing automatic success on hard checks, on tier four even on very hard checks.
To me, this is clearly breaking the design objectives of Bounded Accuracy.
Automatic success invalidates die rolling
A hard skill challenge does not remain hard to solve at higher levels
Allowing everone to meaningful particpate breaks -- challenges for the rogue are impossible for others, challenges for others are a joke for the rogue
In my experience, what makes this even more problematic are cantrips like guidance -- in many cases, you can assume the roll will have 1d4 added to the result. With such boosters, even nearly impossible DCs can become near automatic successes1.
So, I am stumped. How does Expertise make any sense, given the objectives of bounded accuracy?
P.S. For my games, I have resigned myself to accept the fact that Expertise is effectively like magic. These characters just will detect all the secret doors, and will never be heard or seen when sneaking. That is fine. Magic can do similar things, it is not breaking the game.
P.S.S I apologize this came across a bit ranty. After reading up more on how to pose good designer intent questions, I realize it might have been better to frame it as a question on how to balance Expertise. I'll leave it stand as is, because changing it now would invalidate Ryan C. Thomas's excellent answer.
1 The same applies to magic items. In my experience groups tend to reinforce characters when they distribute magic items. So a skill enhancement item (like gloves of thievery, boots of elvenkind, eyes of the eagle etc.) will likely go to the expertise character. These items by themselves contribute to breaking bounded accuracy -- they grant +5 or even +10 bonuses, way more than the at best +3 bonuses from magic weapons. However, I think Bounded Accuracy assumes a game where magic items are optional, so maybe it is more appropriate to look at this without them.