Sure the rogue/wizard is an extreme example, but it is only part of the problem. One of the ideas with BA was to cap things around 30. With the normal +11 max, that works, but with expertise is blows up to +17. This increased both the floor and ceiling too much IMO. The simplest solutions are a flat +2 bonus, advantage, or half-prof (round down) bonus.
Otherwise, you have rogues better at grappling than fighters, better at medicine than clerics, better at arcana than wizards, and so on. Yeah, rogues (and bards) are supposed to be the skill-monkeys, but IMO something like Jack-of-All-Trades more represents that.
Of course, other classes have features in some subclasses that grant the equivalent of expertise (and why NOT just call it what it is for crying out loud???) such as Blessings of Knowledge for the Knowledge Domain, and the addition of the prodigy feat helps. If you allow it to anyone then you at least remove the problems with rogues and bards being superior at things most people IME don't think they should be the best at (at least potentially).