What I've alays found strange is that it the importance of "choosing the right investor" is regularly thrown around, but where or how does that happen in a demo day type experience.

I'm somewhat assuming that the best companies have already lined up the right investors for their business before demo day, and perhaps use demo day frenzy to drive the size of the round, but what does this do to the trust with the investor as well?

Specific to YC, I suspect investors have the trust that YC has done the diligence over the previous months, and that they aren't going to put their stamp on a team they know to have issues. It's bad for the YC brand long-term.

Not saying that YC hasn't invested in companies that have had issues, but they are not knowingly putting those companies up as solid YC investments. Companies get kicked out of YC for ethics and other violations.