I'll get on those, I have a few ideas on what function they could perform. And yes, I'm fully aware that "Vestigal" does not mean "Useless" necessarily. In fact, I believe that Vestigality can very well be a part of Micro-evolution but doesn't necessarily leave a trail for true "Macro" in which a "Change of Family or Genus" would be what I would use in place of the slippery concept of "Species".
Now do you agree at least that it's been said by an objective scientific source that Basilosaurus very well may have used those Hip bones for mating and then the connection was that "Other whales mate similarly?" And would you agree that there's not enough research on whale mating to say that the hip bones aren't used for such? Would it be fair to say that one cannot claim the Hip Bones don't have a function necessarily as a matter of fact?
Basilosaurus likely used it's tiny legs as copulatory guides... that is in lining up the male and female so that they could actually perform the deed. (and possibly push rivals out of the way) This is not a problem for modern whales for very interesting but not very often talked about reasons.
Whale mating is actually pretty well studied (at least as well as it can be) and whales don't mate with any "hip action" in the way we would think of it.
A male whale's penis is more like an elephants trunk than an elephants penis...it is highly mobile and can move in any direction and even wrap itself around things. This means that the male and female don't have to line up with each other to mate. They can mate in essentially any position except perhaps with the male directly above the female.
In this sense then no... modern whales don't mate similarly to Basilosaurus. Unless you mean that they did it in the water.
Again... the subject of whale penises isn't exactly a hot topic of discussion in most places, so it's understandable that it may be thought of as a "poorly studied" subject it certainly is a place where there is a lot of room for more research. But given that we have plenty of captive bred whales and dolphins it's not exactly an area that is going to be a total mystery.
The real areas that haven't been researched enough are particular mating habits of individual species. We understand the anatomy of it.
The only reason I personally know about it, is that I was fortunate enough to get to hear a lecture on the subject from one of the top whale anatomists.
wa:do