In many respects 5E tried to keep this logic in the form of bounded accuracy by making level adjustments on success down. So unlike 4E where there was a fairly relentless level-based scaling, 5E tries to keep large degrees of scaling to hit points and class features, and keep most bonuses within a smaller operating range overall.
However, the areas I'm talking about---save DCs for some monsters and, especially, skill bonuses for some characters---they just blew it. We haven't talked about it much in this thread, but IMO the skill system has more problems than saves, which I think could be handled by keeping most save DCs below 20 and just making some of the boss monsters tougher in other ways than cranking up save DCs, although the fact that the gap between strong saves and weak saves gets extremely wide even by level 10 is a bit of a problem.
Expertise itself is fine if you use it to become good at a skill you're ordinarily not supposed to be. For example, the Wisdom 10 Rogue who uses Expertise to rock out Perception is not going to be too crazy. The final ability will be on par with other characters who are just proficient in an ordinary way and have a strong stat. However, when Expertise is used to, say, boost Thieves' Tools, essentially no lock or trap is much of a barrier to that character without heavy contrivance. Nor is it often perceived as worth it for any other character to pursue having proficiency in that. Yes I could triple lock everything and make sure every encounter involving a lock has some kind of countdown timer that means the rogue is always under time pressure or present dilemmas that push someone else to have to make those rolls... or I could take the path of least resistance and DC creep. I'd simply be better off without doing that and making Expertise cool some other way.
If you want a really simple fix, just making Expertise grant Advantage instead of doubling the proficiency bonus would rein in the numbers. It would be undeniably useful and clearly make the character more effective than normal due to making a low roll less likely. There may be other ways to make use of this, too. If more skill checks were like skill challenges, i.e. requiring a few successes to fully complete, the character rolling with Advantage could tally up successes on both dice, meaning that tasks could be accomplished more quickly.
Example:Using just Expertise = Advantage here. Louvin Lightfinger, thief extraordinaire, has Expertise with Thieves Tools. He's picking a lock in the workshop of Gnimbly Gnob the Gnomish jeweler. He has a bonus of +7 (18 Dex, proficiency of +3). The fairly complex lock has a DC of 15 and requires 3 successes to pick and a failure represents the lock being stuck permanently. He rolls 18 and 18 on the first two dice, a success. This takes a minute. The next minute he rolls a 2 and 11. He breathes a sigh of relief that he's rolling two dice and can ignore that 2....
I'm sure there are holes in this---I mean I just thought of it at the moment so it'd need testing and calibration---but it represents Expertise not as a quantitative difference simply by making the numbers higher (and thus tempting the DM into DC creep to boost up perceived challenge) but by making a more qualitative difference. Here Expertise means you're much more reliable than someone with just ordinary proficiency. The big thing is that Advantage has relatively limited impact in that it does not allow you to roll above what you could ordinarily accomplish, while still being undeniably beneficial.
As I've said many times, 4E had many good ideas. I think some of them ended up being taken too far. For instance, it was too relentlessly game balanced for my taste. I felt when I ran it, especially, the constant and heavy hand of the designer, which I did not like. I enjoyed playing 4E much more than running it, which I found an exercise in frustration as I am not the sort of person who adapts myself to someone else's vision. It also seemed to bring out the rules lawyer in players, even ones who'd not been especially rules lawyer-y before.
But all that aside, 4E had a number of good ideas and WotC kept a number of them in 5E, though in some cases I'm not sure they did it as well as they could in some spots.