Providers do this because it's a bargaining chip when negotiating rates with insurers. An insurer will say "this procedure should only cost $100". The provider will counter by showing that their "list" price for the procedure is $1200. They'll compromise on $250 and some uninsured schmuck will go bankrupt trying to cover the "list" prices.

It continues because 1) Having absurd prices is not illegal. Of course absurd prices are usually self-correcting. 2) It's politically infeasible to fix this because it means "someone" (aka the government) has to mandate what the prices should be.