The old timers must be spinning in their graves. I can imagine Bobby Layne or George Blanda snarling “You’re gonna push my WHAT?”
They'd probably ban it but the rules (definition) would be so complicated that it's probably not worth it as players often push teammates in various ways..
It was probably legal in his day. But they didn’t have the name. Then for a long time they outlawed pushing on the player with the ball, but you could push on the “pile” (which led to the famous “hands up” shot from the end of the Icebowl as the guy is trying to show the refs he’s not pushing on the player). Unfortunately that rule was an officiating nightmare, how do you actually tell the difference between pushing on the “pile” and the ball carrier? So they got rid of that rule.
Of course the punchline on the tush push is the Eagles are the only team that’s any good at it. Other teams try, but they fail. Buffalo Bills tried it multiple times in the AFC Championship and failed every time. Which I think is the real reason teams want to get rid of it. “We can’t do it for beans, so we don’t want you to be able to either”. Also QBs say it’s really not a fun play and rather painful getting squished between linemen like that.