Having a compliance test whether a set of features is implemented correctly is nearly always a very good idea (I really have to think seriously to even find examples where it is not. There is a reason why some development teams even make it as a central principle for managing software development (TDD - test-driven development). I am of course aware of the fact that the features tested with Acid3 were chosen such that every browser of that time looked bad in Acid3. This makes Acid3 a little political, but not wrong.
A test suite can become "old-fashioned" if you will have to look hard for an implementation that fails to comply with it. Acid1 has been belonging into this category for a long time and today I would also put Acid2 into this category.
But since we can now find implementations (Chrome, Firefox) which describe themselves as cutting edge in implementing new features (opposed to Edge) and fail the test, this shows to me that Acid3 has not become "old-fashioned". The issue shown by the 97/100 in this test could also show a serious issue in backwards compatibility of the standards that it tests (cf. https://news.ycombinator.com/item?id=15258700) - and this is something that should be analyzed carefully. This alone still makes Acid3 useful, I think.