There's that awkward moment where the announcer goes "Mr. and Mrs... Uh. <both their names>"
The "problems" you describe are just...nonexistent, and really not a big deal. I have literally never encountered confusion about our marital status, problems with forms, or difficulty being introduced.
In fact, it’s worked well enough for us that if we were to have another child we’d consider giving him or her a different last name again instead of picking one of the three we already have.
(The only reason we sometimes wish she'd change her name is that hers is extremely common, and so she's constantly getting mixups with other people with the same name and has to sign things every time we buy a house or get a loan, etc. to say she isn't that other XXX YYY that has the bad credit rating or outstanding loan or criminal record, etc.)
What's weird is these are people with generally left-wing political views, and socially liberal on most things. But on women's issues, pretty backwards. It weirds me out.