The last time this happened the Play-in game was born. I just think you'll see a further expansion of the First Four.

Bids only disappear from high-major conferences only when lower division teams win the tournament.  When Georgia finished 10th or so in the SEC a few years back and won their tournament a bid vanished.  But this is pretty rare.  It just gives two chances for the very improbable to happen instead of one.

Bids rarely disappear in low-major tournaments either because no team in the league has qualified itself most of the time and it will be a 1 bid league no matter who wins.

Where they vanish most often is mid-major leagues where 1-3 teams have usually already qualified themselves.  Unfortunately, the MAC had been rating as a good low-major league the past 5 or 6 years rather than a league that has a rating good enough for teams to have real chances to earn at-large bids.  I know we haven't earned an at-large bid for a while but it was due to high parity and bad luck.  With the ratings the conference had in the late 90s and early 2000s most conferences on that level were getting them pretty often.

Until today Southern Mississippi and UMass had the chance to be bid-stealers because they were still alive and not listed currently on anybody's list of teams in.  But even this is a stretch of what a bid stealer is because if you added the wins needed to win their tournament to their resumes they might have been at-large worthy anyway and they don't end up going ahead of a team ranked below them.

I thought there was a period of time when new conferences weren't given automatic bids.  I may be mistaken though.

"Great" West only has five teams (and five really crappy teams at that); a conference needs at least eight to be considered for an auto bid.  But these aren't "new" conferences so all they really need to do is ask.