I can't be bothered to quote everyone who said they thought Van Nistelrooij did well at PSV - but as
@KirkDuyt already said, he didn't. He did won the Dutch charity shield and cup, but both are seen as minor trophies. PSV is all about the title and making it far in Europe, and Van Nistelrooij didn't achieve much either way. Granted, he was up against a very strong Feyenoord side, but the problem more generally was that the team made little progress in the course of the season and didn't have a clear style. The fans weren't behind him, and it seems eventually he didn't have the full support from the squad anymore either. He actually quit himself (one match before the end of the season), but otherwise he might have been fired after the last match.
All that to say that Van Nistelrooij thus isn't really coming from a position of strength. He also actually didn't want the PSV job initially, cause he thought himself that he wasn't ready to be head coach yet; he had to be talked into it by PSV's management. (He was coaching PSV's youth team at the time, I think it was.) So he might actually be interested in working under Ten Hag, to keep learning and re-establish himself. I would think he'd be there to replace Van der Gaag though; being just an attacking coach does really seem beneath his level of experience. (And I did see news about Van der Gaag not being too much like Ten Hag and hence not complementing him much; so I could imagine United wanting a different profile there. I don't know what Van Nistelrooij is like as a coach in that regard though.)
@Eendracht maakt macht is the PSV specialist btw.