You are right - non-possession football is both mentally and physically more draining. You are continually chasing and having to try and anticipate what the opposition are going to instead of controlling your own destiny with the ball. I suspect that mental tiredness is what is leading to quite a lot of late goals conceded.I would present an argument that its the way we play.. If you're being forced to do 100m sprints you get more tired than playing football.
It's also why we get lots of muscle injuries
****ing hell that is beyond ****.