Shinji tried to alter the barrier to make an exception for air, but by the time he tried he was too late.
He also wouldn't have died from suffocating, and the manifestation would've ended when he fell unconscious anyway. Problem is all the crest worms in the house which are drawn to magical energy...
As for the air pressure, Nasuverse protagonists have a habit of ignoring crucial things that will lead to their death in Dead Ends.
Shirou didn't realize his feet had been eaten in one ending.

Part 6