dumb question but do the airport gates get "too full" if all plans are grounded? Do airports sort of expect some constant turnover to have enough open gates to service everything? Do you end up with a line of plans waiting for a gate?

Very, very much yes. Most busy airports will start having problems with gate capacity due to just normal delays. We definitely don't have the capacity to have every active flight in the country parked at a gate.

Based on my current experience on the ground at AUS, yes.

Gates were quickly full, ground ops to pull empty planes off gates takes quite a while, and about 90 mins later, we are pulling into our scheduled gate.

Not an expert but my guess:

They don't spend a dollar more than they need to so extra gates for this would be quite the luxury. I guess what they need though is apron space or hangar space for the extra planes and the number of gates won't matter so much.