This is one of those issues where I think the theoretical doesn't match the experiential.
I think on paper people look at expertise and believe there will be a meaningful number of instances where the ability violates the principals of bounded accuracy in a way which would harm their games.
But in experience, after a lot of people have used this ability in practice, I've almost never seen anyone state they found it messed with their fun, with their assumptions about a challenge's difficulty, or any other aspect of the game.
I think the gap comes down to the fact this game has much more forgiving tolerances built into it than is assumed. The bounded accuracy numbers, particularly for skills, just are not that firm. There is enough room at the top and bottom end of the challenge charts to handle a bump like this without it blowing any built-in protections.
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An example: The idea that the rogue who focuses on Arcana with expertise in Arcana outshines a Wizard with the Arcana skill.
First, the instances of this coming up are extremely rare. Rogues alone are somewhat rare (many consider them lower in power overall, particularly relative to the Wizard), choosing a high intelligence for a rogue would be rare and choosing one that is AS HIGH as a Wizard would be rarer still. And then choosing Arcana as one of their very few skills to apply expertise to (instead of something like perception, which everyone wants, or rogue-like skills such as slight of hand or acrobatics or the charisma based skills) is even more rare.
The combination is so rare that the effect on the game becomes fairly meaingless as Arcana checks will never be set so high as to assume a rogue, with a high intelligence, proficiency in arcana, and expertise in arcana. Sure, they could, in theory, have a +15 in Arcana. But the tolerances of the game were already set expecting a Wizard with a high intelligence and proficiency to be able to hit those challenges already (which will max out around a DC 30). So what, the rogue is hitting those challenges "even more"? In-game, it essentially isn't a big deal.
The assumption that you have a DC 35+ for something just...isn't a good one. 5e isn't like 3e. The DCs don't continue to go up like that over levels. They max out at DC 30 (nearly impossible) on a fixed chart which applies for all levels, 1-20, and most checks will be DC 20 (hard) or lower throughout the game.
Your 13th level Wizard will have probably a +10 bonus. Your rogue with expertise in Arcana who decided to not dump intelligence will probably have around a +12 bonus (because who are we kidding - you didn't max out intelligence and it was probably your third-highest stat).
OK, and? Most of your checks are at a DC 20 (hard) or lower. Both of you will make the check most of the time anyway. Your rogue might make it slightly more often than you, at the sacrifice of their precious expertise ability use for that skill...which is fine. You're likely playing up this aspect of your rogue in-game because the role-playing aspect would become meaningful if you're a rogue with expertise in arcana. The wizard didn't sacrifice nearly as much to get to nearly the same achievement.
Both of you can potentially make even the most nearly impossible check with luck, so in-game this just isn't breaking anything meaningful and you should be having fun with your arcana-focused rogue who probably has a penchant for Indiana Jones type tomb raiding for arcane objects of power without stepping on the toes of your Wizard who is regularly breaking the laws of physics with their spells. Both of you can make most Arcana checks, and the Wizard is probably happy he has someone else in the party able to make these checks if he or she happens to fail one because most parties don't have that kind of backup for that particular skill. I doubt the Wizard's player will feel like their being outshone. After all, it's not a counterspell check or a fireball - it's mostly just figuring stuff out concerning arcane things, which helps the adventure move along.
