As with all else, "It Depends". Please see the latest article from Tony on the subject.
http://www.sqlservercentral.com/articles/Editorial/105414/
I agree that they are a panacea for nothing and usually cause a whole lot of trouble especially for those who might not be well practiced at them. But, they are a tool that can be used very successfully for certain things.
I also wouldn't necessarily call the tables given by the OP EAV or OTLT any more than I'd call a check account and EAB or OTLT. "IT DEPENDS!" 😉
--Jeff Moden
Change is inevitable... Change for the better is not.