I totally agree!
I also want to add here that it's not about Gegenpress or pressing in general. The point is that in real life the one who doesn't have the ball gets more tired than the one who does.
We first need to know how each system works in real life and then say whatever. If the team's pressing is efficient then it is the other team that should be tired. In Gegenpress the pressing is done as a team (not individually) and in compact spaces, which the system creates out of possession, so that it is more successful.
Then come the negatives of stifling pressing which are:
Ball management - if you lose the ball soon then players have to run back to press. ( this is where the fatigue comes in )
If you combine very aggresive pressing out of possession and tiki-taka in possession then you have the best system in the world. Look Man City right now.
Player characteristics - if your players don't have certain characteristics as units, as a team and also good team cohesion to be able to faithfully follow the progression of the game and know how to move out of possession then pressing will failed and might produce some injuries too.
Training - good recovery and a schedule in general that will keep them fresh for each game. Look Liverpool the last few years.