Trump knew full well who the holdovers were and where they were......even before setting foot inside the WH.
My sense is he left them there for a good reason......
<><> who did they talk to?
<><> who was contacting them?
<><> what agencies were they in touch with?
.....and so on, and so forth, ad infinitum, ad nauseaum......
I don't think they stayed in place so Trump could entrap them. Rush said on his show last week, that McMasters was advised to cut the NSC staff and he did not and Trump can't focus on everything. I don't think the size of the NSC staff was a priority point when he entered office.
That does seem to be a consequence of the way things played out. In the interim Hillary’s deranged actions have left her with no supporters and all the spying and corruption being exposed has soiled Obama’s reputation. so now PresidentTrump having his base secured can go after the crooks in the Obama administration namely Obama Clinton Brennan Comey clapper. As much as I wanted him to go after Hillary he probably couldn’t have done it right after the election without the public being very upset he definitely couldn’t have gone after Obama. I wish he still would have fired a bunch of those Obama political appointees though. Washington owned slaves, Abraham Lincoln had a crazy wife who liked the theater, no president is perfect