If you don't peddle it as the real solution with zero evidence or as anything other than an interesting thought experiment, why not? He's not starting a cult based on multiple big bangs. I think it's fine.
I should have also been a little more specific with the "the math doesn't prove or disprove it" as in, "the math as it currently stands does not prove or disprove it." Which is true of a lot of theories in physics. There is a possibility and the math and experimentation isn't there yet to decide if the theory is correct or not. Not that the math will never come, but the equations are not there today.
To answer the question, within reasonable limits, yes. If it is a thought experiment to provoke looking at a problem a different way, it could be useful. While Fred Hoyle's steady state theory didn't hold much water, using it as a basis to analyze certain problems, he was able to held figure out Nucleosynthesis. The problem is knowing the reasonable limits. Like, don't let it consume your entire life's work and use it as a means to analyze a problem from a different angle.
In context of Roger Penrose, it may be illuminating. Right now, I imagine most are trying to solve the problem starting at the big bang and working backwards. Penrose is essentially trying to pick some arbitrary potential solution and asking, "if this is true, what else must be true" and seeing if he can work his way forward to the Big Bang or not.
They are not unfalsifiable, just unprovable. Unfalsifiable means they can not be proven wrong even with additional data, whereas these we just can't prove nor denie with current data, but we could if we found more data.
This is such a common trope. Erasthenes observed the Earth must be round using shadows over 2 thousand years ago. There was never an intellectual controversy about it before internet dupes fell for an obvious prank.
There is no historical record of such controversy. It's an easy question to answer with basic astronomy and geometry. The controversy is a modern manufacture and the cartoon trope of old timey misconceptions about the shape of Earth is not based on evidence. Those in a position to ask the question have always been in a position to reach the obvious answer.
I would say, if you go back 2,000 years, most people probably never considered the question or cared. The ones who did were a small number of intellectuals. At some point, there probably was a debate among those. The peasants out in the field? Didn't know and probably didn't care and didn't matter.
The point is, it's an easy question to answer and it was as soon as it was posited. There was never a controversy recorded before this internet forum prank we have. The trope that people in olden times (usually some sort of renaissance/medieval mashup) were stupidly believing Earth had a flat shape has no basis in historical record.
