The so-called disaster is an outcome of quantum physics which is - justly - applied to cosmology, but of course would need some dedicated care when doing so. As limited as the influence of quantum physics is in our usual everyday environment, the quantum realm has also just a limited impact on cosmology - and it certainly doesn't rule out our universe being the result of inflation. It just appears as if Paul Steinhardt isn't a friend of the multiverse idea, as opposed to a vast number of scientists.

Fantastic argument based on comparison with progressively marginally younger universes etc. (Not sure how many viewers will understand measure and measure theory though, so this bit might need to be reframed for clarity in any repeat lectures.)

If, as Paul Steinhardt claims, the inflation theory is truly untestable via scentific rigour, then it devolves into a belief system that requires an act of faith from its advocates. Not susceptible to intellectual investigation and can therefore have no place in science.