No, but the "All Pro" team should be built like a team. But just like the pro bowl they vote for the players based on positions that dont really exist anymore.
No it shouldn't. That would be an absurdly subjective exercise with absolutely no meaning whatsoever as an accolade. Is there an all pro scheme?
"Sorry, we picked a quarterback so most of the other guys don't fit in the salary cap so we've got some rookies in there".
All pro is there to reward positional excellence.