Being popular isn't the same as being correct. Not that I think Husserl himself was so far off track (one can't fairly criticize the prescient for not having the advantage of later discoveries), but perhaps due to practitioners lacking the acumen of Husserl himself, the corrupted versions adopted by social scientists seem mostly to me to motivate retreat from "science". (Social sciences have always struggled with actually being sciences: it's far easier to give up and declare "here we do it this other way" than meet the prerequisites for inquiry that we normally term "science". Patting oneself on the back for saying "intersubjectivity" a lot is not as useful a way to build reliable knowledge as having an sample size with sufficient statistical power.)

I agree that the general strategy of looking-at-experience is popular, and it's probably the most likely to deliver a satisfying account--I didn't mean to imply (but probably did) that you surely can't terminate in the "contents of consciousness". Rather, I intended to convey that it isn't a solved problem, so that pointing that way is more like the start of a conversation than the end of a well-grounded argument. Phenomenology itself doesn't get you very far if you can't leverage your way up to epistemology and the interplay between the two, which in turn doesn't do all that much if you can't make it to ontology.