Do talent show programmes film lots of footage or is it set up? I keep watching auditions from talent shows. It seems like they have an interview process before each audition and apparently 'randomly' select them before they even enter the arena to do the audition.

Do the crews just film lots of footage of every freaking contestant (HD, 1 minute per contestant avg., hundreds of contestants) or do they do a process before-hand of deciding who will end up on the final cut (entertainment value ). 

Surely if all the contestants have interviews where seemingly 'random' questions that reveal information on their backstories that would take up a lot of storage and be a real pain for the teams who have to edit it all together for the TV cut?

I know for a fact that they interview each contestant before hand (not always filmed - I think) so that the judges know what questions to ask the contestants (example: "is this a cover song or are you a songwriter" - contestant before hand said they were a songwriting, "what do you cuirrently do" - contestant is on show to escape menial, obscure, job).

I'm not sure if this is the right stackexchange site but it seems close enough.

tl;dr - Do talent show (audition based entertainment) programmes film lots of footage of each contestant in a hope that the contestant is entertaining (like interview before audition - outside arena - cliché shots of the contestants sitting around looking nervous) or do they have a huge process of selecting out acts that have entertainment value (based on some form of prerequisite audition tape or whatever) and then only selecting them?

This is a question I ponder every time I watch these shows.

I have a feeling the answer is a lot simpler than the ideas I've proposed here.
I've shot live events for the past 5 years, and had a few friends get on (and actually pretty far in) both American Idol and The Voice. There is a series of auditions way before contestants ever get in front of a studio camera, let alone a TV audience. Most auditions are not filmed, unless it is recorded by the casting directors/producers purely for their reference, usually with a simple handycam.

Yes, some auditions are staged a certain way, but not usually scripted. The nervous shots and emotional cut-aways you mentioned are almost always staged, shot after the fact, and then edited in a way that lets the audience project meaning onto the shot. The exception of course being when producers know a big event is about to take place (e.g. put a cameraman in the green room right before the contestant goes on stage.)

At this point it becomes a matter of efficiently handling your media so producers can quickly call up a shot that, even if they haven't seen it yet, they know it exists. That's why digital intermediates on set are worth their weight in gold for "reality" TV shows.

If it's a live show, there are many cameramen all wearing earpieces, ready to take direction from producers on who/what to cover and when. Then you have a big team of people behind the scenes watching what every camera sees and punching up the appropriate shots to the audience. So in this sense only, yes they just shoot a bunch of footage. But a live streaming video is a bit different than recording to hard disc.