There is very little you can do to pick up good audio for audience questions. Reporters are simply not going to wait for a mic runner to get to them before asking a question, you can’t give each one a mic, they’re not going to queue up behind standing mics, no single mic is going to pick up broadcast-standard quality audio for an entire room of reporters, nor would a human-controlled shotgun or parabolic mic.
The best solution is hanging choir mics (a group of tiny little mics hanging from the ceiling), but that is something generally built into a room. The production conference room I ran had a section in front of the stage with mics built into the conference tables. Even when they weren’t pumping feedback into the room they were a bitch to isolate a voice on the fly.
All the other solutions I can think of require a load of money, time, or space to use, and just not always available on short notice.
Sometimes you do hear the reporter’s voice in the middle of their question when someone gets a mic in range.
One more thought on edit: It’s only recently that press conferences were viewed regularly by the general public. They are only now shifting away from catering to print media.