I think the most important strategy for any magician wanting to "Spread their name" with AGT is ... not to use AGT to establish themselves. Shin Lim was already pretty successful before he set foot on that stage. Matt Franco was already doing well for himself. Aiden Sinclair was already doing well with the Stanley. Dan Sperry has said he literally never planned to try to win, he only wanted to be sure to get in one televised round so he could say "As seen on national TV".
Here's the thing - AGT's contract is brutal. In it they literally state they can do whatever they want with your likeness. Meaning they can (and they have done this in the past) take the footage from one performer, and mix it in with the audience and judge reactions from a totally different performance, to make it look like that performer bombed even if they did well. What you see on AGT is totally fabricated. Oh yeah, remember I mentioned Dan Sperry above? At least one of his aired spots (The coin trick he did on the edge of the stage), was his rehearsal, not his live performance. The live performance has much more blood.
So for someone who is not yet established, that could, in all reality, end their career. In the very least it's a massive set back if they decide they want you to be the fool for that episode. Side note - this is why the judges wear the same clothes frequently, so it's easier to edit the footage together if needs be.
Oh - and they want a narrative they can tell. A back story - which they decide what parts to emphasize. Eric Jones comes to mind. Aiden Sinclair, as well. Though I still think Aiden has one of the absolute best back stories in magic.
P&T is a much, much better show for someone who isn't super well established because what you see on that show is what actually happens. Other than some editing for time (P&T actually discuss for much longer than they tend to show on TV, for example). P&T genuinely want to help other magicians, so they do their best to make people look good, or at least accurately represent them.
A) There are probably too many magicians. With magic, most of our material is at its core shared with that of other magicians. The preliminary judges (and then even the ones we see on TV) and the crew all have to go through thousands of auditions a day.
AGT auditions are split up between a decently large number of judges. You get funneled through various doors to various audition spots (And some of them are auto-denied, from what I'm told). If you're not one of the talents they specifically recruit for the season, you'll do 3-6 auditions before you're even in the same buildings as the 'main' celebrity judges.
Other than that, I agree - they probably see a huge number of really interchangeable magicians.
B) A card trick is never made for a bunch of TVs. It's made for a live audience. It must be near impossible to see from the back of the live audience if the magician does it for a camera, and your left watching it on the big screen (at which point it'll be weird for the judges). If the trick is performed for the audience, the camera is stuck because they can't film everything. It just becomes a hassle to film and show on TV.
A good production company can over come this and AGT has a nigh unlimited budget. The thing to remember is that you can't worry too much about the values of the cards - you have to rely on the audience feeling in sync with the volunteer. Mac King does cards across on a grand stage and it works because it's not the cards themselves that matter - it's the count, and his cloak of invisibility.