Lack of hotel space is not really a new issue with the Olympics. Rooms were first being offered nearly 2 years ago at all major hotels (and yes, of course, they were booked fast), cruiseships, house rentals, etc. Unfortunately the Olympics are not an event where you can just show up without planning far in the past. It's not a sudden thing, people have known about these Olympics for 7 years.
There will be plenty of "public" at the games. They will, however, have planned to be coming for a couple of years now
Next we'll be hearing surprise that planes arriving and departing at YVR are full, and are more expensive, during the Olympics.