Which is also a somewhat faulty logic. The paper assumes that because a machine can have its lifetime extended from 10 to 20 years, its inevitable to extend it to 1000 years or infinite timespans.
But with every incremental step your faced with newer more complex problems, and you hit limits you didn’t previously know existed.
It might be possible…or it might be impossible and we just don’t know yet.
I just scanned quickly through the paper, but I think that's a simplification that doesn't really alter the main conclusion.
The underlying assumption is that a time traveler can use a time machine to enact an infinite number of changes to a timeline. Even with an unbreakable machine, a time traveler won't be able to do so, because sooner or later they would die.
But as long as we assume that the typical amount of changes introduced by a traveler is the same across all travelers and timelines, this would just amount to an overall rescaling of all transition probabilities, which is already accounted for in the paper.
My gut feeling is that also if you allow variation in the number of changes an individual TM can introduce in a timeline, as long as that variations are not correlated with the number of TM present in that timeline, you should get the same asymptotic behavior.
IMO, this is just somebody having a bit of fun with a toy model that is being given more relevance than it deserves by a popular science magazine. It may even be polished enough to get published in an actual journal (you don't publish on arxiv, you just upload to it. As the name implies, it's not a journal but an archive.), but in the end it's just a bit of math dressing around the idea that if alterations to a timeline introduced by time travel are equally likely to create a timeline with a lower or greater number of TM, sooner or later you are bound to end in a timeline with 0 TM, at which point the process stops.
Interestingly, that isn't actually true. The differences are miniscule but not nonexistent. You travel through time differently on a plane versus sitting on a couch, or taking a walk versus taking the train.
It's still 60s every minute. There is just not an absolute time that flows equally for everyone, so my 60s are different from your 60s.