Firstly, I don't NEED to do anything, so let's that get that out of the way. I can look up the consecutive innings compared to the other top closers though, sure, since that's an easy enough thing to do.
Easy innings in unquantifiable unless you simply operationalize easier innings as non-save situations. It was a throw-away comment so I won't even get into it since it's not really important.
As far as age, I did a quick look at the top closers over the last 2 decades (Rivera, Hoffman, Jansen, etc.) None have pitched as many MLB innings before the age of 22 as Osuna has. Is there evidence to suggest this will definitely result in injury? Not at present. But the fact that it hasn't been done very often or at all, is a great reason for uncertainty.
It's like saying has a starting pitcher in the modern era ever pitched 400+ innings in a season? The answer is probably no. Is there evidence that pitching that many innings in a season can cause injury? Probably not, but you probably don't want to test it out either.