There is always tons of excess last-minute hotel inventory just before the Olympics. Doesn't matter what city.
1) The normal tourist crowds unconnected with the Olympics defer their travel
2) Businesses move venues for meetings and conferences to other cities, or defer until after the Games.
3) Corporations that advance block-book rooms to entertain clients from around the world and for employee rewards, don't have the numbers of guests materialize and release them back (some sell directly to any takers)

The amount of Olympic-connected traffic generated, does not more than offset all the other business lost or foregone during this time. Those unconnected with the Olympics definitely aren't going to deal with the extra hassles and high costs to try to co-exist during this time.

The experienced Olympics-attendees learned this long ago, and generally don't start looking for a room in the host city until one month before the start of the Games, some even wait until only 2 weeks before. Those who advance-booked non-refundable rooms at very high cost are the losers, but it's of their own doing.