The National Football League is played in the United States. The National Rugby League plays in Australia and New Zealand. Essentially, the tush push is an adopted form of rugby play. Which sport will be poached next to 'better' North American style football? Soccer?
The quarterback sneak has been a part of football for many decades. It is definitely not 100% safe for players but I would say it is safer than the tush push.
Football is a copycat sport. When will the proliferation of the tush push begin filtering down to the college and high school levels? Will coaches begin evaluating players who can squat x-amount of pounds and have a decent enough arm? How soon will more coaches mirror Jets' head coach Robert Saleh describing opposing quarterbacks (e.g. Jalen Hurts) as,
"wearing a bulletproof vest when you look at him, he's got all that padding on?" Will a significant tush push related injury cause anyone to stop and re-evaluate its use?
I do not know. Perhaps Roger Goodell can make an argument with the owners using a player safety angle. And as everyone already knows, the NFL is ALL about player safety.