One small wrinkle: what if there's an old existing compound that seems to work well for an different indication than it was originally approved for? It would be good to run the phase 3 trial (possibly phase 2 as well) but that's gonna cost a ton of money. Maybe the government does it, or maybe we let people extend a patent for a new indication, freeing up government research money for the much trickier problem of understanding fundamental disease mechanisms.

There are of course good arguments against, but there's at least some good arguments to allow limited patent extensions.