I see too much potential for this to be abused. A 4th and 15 is easier to convert than an onside kick, even before the kick off rule changes.
It also favors gunslinging offensive teams over teams that rely on shorter passes and their run game. Just doesn't feel balanced.
A team like the Chiefs would greatly benefit from this rule, while a team like the Titans would have their best offensive weapon be almost useless.
It also favors teams that are better at defending the pass over ones that are stronger at defending against the run.
The onside kick was a small part of the game, that was rarely attempted outside of when necessary. I can see the 4th and 15 being a staple of many team's offenses who might use it much more than we are anticipating.
Even if the limit is set a two times per game, I expect we would see way more 4th and 15 attempts than we ever saw with onside kicks.
I don't like how converting an onside kick is nearly impossible today. Team's need to be able to come back from 2 scores down late in games. But I think there has to be a better way to fix the problem.