Space

A couple notes:

First, renormalizarion was hand-wavy when it was first introduced, but it has since been made mathematically rigorous. Additionally, renormalization is a mathematical process to make a theory self-consistent. If you consider it an odd idea because it is physically nonsense, I would caution against forming a physical intuition from any given accurate mathematical model. Especially with fundamental quantum mechanics—there’s a reason why there are several interpretations of QM and have been for a century.

Second, and arguably more importantly: this ScienceDaily article is extremely misleading. The original paper (linked by OP in another comment) says

This is a scenario where the inflaton does not exist, and thus opens up the possibility to provide a picture of inflation that is model independent

So the paper does rid itself of the inflaton field, which is, as you said, a bit of a hand-wave. Crucially, however, it does not abandon inflation—in fact, it explains those “for no reason”s that you mentioned.