I have used it on several occasions assuming that it was stronger (per the marketing) than standard PVA wood glues such as Titebond.
Because of the much-publicised results of one glue shoot-out in a major woodworking publication Gorilla actually had to change their claims and the marketing blurb for their original Gorilla Glue. The display items, and even the label itself I think, used to say "the strongest glue on planet Earth" or words to that effect. Since that was shown not to be the case they don't use that tagline any more.
I was reading an article the other day that says that for other than end to end wood joints, its strength is basically the same as PVA.
Testing by various parties has shown that polyurethane glue doesn't bond more strongly than other glue types. Obviously the major comparison point is either yellow or white types of PVA. Just to be clear, this has become a little over-stated in the years since.... something that tends to get forgotten or is merely not stated is that the comparative strength of the bonds is technically irrelevant since for most joints the weakest of them creates a bond as strong or stronger than the wood itself.
Note that it's possible that PU is not stronger for joining end grain either. This is the weakest glue joint as most of us know, but various steps can be taken to help get a better joint with whatever glue is being used (e.g. with PVA or hide glue, 'sizing' the joint with thinned glue prior to the application of the full-strength glue just before the joint is brought together and clamped).
My question then is are there actual applications for which Polyurethane glue would be the glue of choice?
This unfortunately is partly an opinion-based thing. There are specific jobs for which a PU glue is chosen by one person that another would happily use the right type of yellow PVA for, others would go with epoxy and still others would prefer a urea-formaldehyde glue.
You could legitimately say there are no applications for which PU is the glue of choice because there is nothing for which it is the sole best option. It's just one of a number of possible good choices.
Basically when it comes down to the bond created PU is strong enough, so on that basis you could pick it.
If it comes down to how waterproof the joint needs to be you might go with PU, but again there are other glues at least as waterproof.
One very key advantage of PU is that it allows fairly leisurely glue ups because it's not drying out on the surface as soon as you've applied it as PVA is, but this is partly dependent on relative humidity and the MC of the wood. Those in drier circumstances will find it much more forgiving in this regard compared to those living somewhere damp.
One additional property of polyurethane adhesives is not purely about wood, they will stick to dissimilar materials. So you could use PU to bond a steel plate to wood for example. But yet again, there are other glues that can do that too.
However, that same article stated that the foam matrix it creates is not very strong.
Yes that's correct. It's easy enough to get an idea of how weak the foam matrix is by how little effort is needed to remove PU foam-out (compared to fully hardened yellow glue squeeze-out for example).
The fact that it foams up is misleading and can lead to the erroneous belief that you had yourself that it is a good gap-filling adhesive, but that is very much not the case because the foam has little strength.
If you do need gap filling, epoxy is probably the glue of choice. Although urea-formaldehyde glues also have some gap-filling ability they're trickier to use, with a narrower temperature range and requiring much more time with clamp pressure applied.
Final note: because polyurethane glue is set by moisture it is notorious for going off in the bottle after the seal is broken. So if you do want to use it I would make a point about working through the contents of the bottle in good time, or you'll go to use it and find that it won't come out the nozzle any more.
If you're a leisure woodworker who only does the occasional job and you might not get a chance to use the glue again for weeks or even months I would strongly recommend you look at other glues instead.