PUAs make claims that are based on naturalistic observation, and hence lack rigorous scientific backing.

Correct. Naturalistic observation is indeed inferior to rigorous science on mating preferences... except that the latter doesn't really exist yet, at least not to a degree that it is sufficiently comprehensive and actionable. For people lacking knowledge or experience, naturalistic observation, backed by a little evolutionary psychology still beats, hands down, anything else available right now, especially the most common alternatives (a) blundering around without knowing what you are doing, and (b) following the outdated conventional advice.

Although PUAs should be studying studying science (well, they are, though they are making a few oversimplifications), scientists should also be studying PUAs by taking hypotheses from their theories for testing. But until scientists catch up, a guy need some ideas that are better than his nerdy male brain's model of women combined with the advice of Maxim, his mom, and his friend Joe.

Indeed, I suppose that many LW patrons consider PUAs to be manipulative and immoral, and don't use PUA advice for that reason.

Yes, there are attitudes and techniques in the seduction community that are unethical, or not as ethical as a better option even if they are not actually unethical. In other cases, observers might have overly narrow views of sexual morality, or misunderstand the nature of PUA techniques. Indeed, a blanket rejection of PUA techniques really shows that the person involved doesn't know very much about pickup, because there is plenty of stuff in the community that works and can't be reasonably considered unethical outside of certain religious or radical feminist frameworks.

Personally, I've found that I can add my own moral constraints to what I practice. In fact, I go through implicit calculations about just about everything I do to figure out the expected value of the behavior for both myself and the other person. There is some stuff that I just won't use, even though I know it can be effective (examples upon request). Yet since I have strengths in other areas, I can take this moral stand without destroying my practical success. It is precisely because of my pickup skills that I don't have to make a choice between morality and any kind of success.

Another reason that people on LW would shy away from pickup is that they perceive it as inauthentic and incompatible with their personalities. In response, I would make a similar argument that I made about ethics. If someone is blanketly rejecting pickup out of authenticity, I would suspect that they have an overly narrow notion of their identity. For instance, I had identity-related beliefs such as "I'm not a people person," or "I'm shy," or "I don't do small-talk." Yet such qualities like shyness are really not intrinsic parts of people's personality or identity. Sometimes, to find out what your personality is, you need to stretch it to its limits, and then see what shape it snaps back into.

In my experience, it was possible to take what I wanted from the seduction community and increase my success with women by orders of magnitude, without selling my soul or my identity. This does indeed sound "grandiose," but that doesn't make it not true. YMMV.

Indeed, I suppose that many LW patrons consider PUAs to be manipulative and immoral, and don't use PUA advice for that reason.

I'm yet to see someone who has the skills but doesn't use them for moral reasons. While it's possible to use them immorally, there's nothing about PUA skills that's inherently immoral.

Also, don't forget that LW might have a large number of atomistic loners who don't want to be in relationships, and this might contribute to the high percentage of singles.

It would require a vast deviation from human emotions not to want any kind of relationship (committed or casual, sexual or romantic etc.) with any partner whatsoever. The more likely explanation is that they don't want the kind of relationships with the kind of partners they think they can get, which is basically lack of skills together with perhaps too much rationalization (which is considered wrong thing to do on this site).