1. Approach lots of women
2. Act confident
3. Have entertaining things to say
4. Dress and groom well

...

If all PUA said was those 4 things, it wouldn't be interesting or controversial

This sounds reasonable until you actually think about the four points mentioned in Near mode. Consider:

1. What does approaching lots of women actually look like if done in a logistically sound way? How does this relate to social norms? How does this relate to how feminists would like social norms to be?

2. Observe what actually confident humans do to signal their confidence. Just do.

3. Observe what is actually considered entertaining in a club envrionment that most PUA is designed to work in.

You know most of the things considered disreputable that PUAs advocate are precisely the result of first observing how points one to three actually work in our society and then optimizing to mimic this.

Only dressing and grooming well is probably not inherently controversial and even then pick up artists are mocked for their attempts to reverse engineer fashion that signals what they want to signal.