The race is tightening because Hillary Clinton is an unappealing candidate to Democrats. The party forced her on the rank and file, going into the tank for her and clearing the field. This was fine before the e-mail matter went worse than anticipated, but now, Democrats have to deal with voting for a candidate much of America views as having committed a felony, and whose pointing the finger at Donald Trump's issues with women bring up the Bill Clinton Sex Scandals in voters' minds.
In that vein, I think that many wavering Democrats will, in the end, suck it up for Hillary as I did for Trump. But the polls are tightening NOW because Hillary IS unsavory. And she's an unsavory candidate that the party forced on the rank and file. Her unsavory character, the resurrection of the 1990s Bill Clinton issues, et al, have all but taken away the luster of Hillary becoming the First Woman President.
As I said earlier, there's fairly weak evidence of tightening. There's also absolutely no indication the tightening, if it exists, is because of the factors you identify. The polls show that Trump has perhaps gained a little bit of previously disaffected Republicans "coming home."
If she still wins, she'll be so happy she hung on that the "First" aspect will be minimized. No one really wants to be the First Woman to make it across the Atlantic in a lifeboat.
If she wins by the current polls-projected margin, or even a slightly tightened margin, I don't think the reaction will be anything like, "phew, that was close...so let's not celebrate the 'first woman' thing." Why would they? Some long game to avoid setting high expectations? That's silly.
