While this calculation may help convince about some aspects of some arguments, it isn't necessary for the headline claim. There was always an old issue non-formation (or more accurately partial realization in finite-time or general paradox/etc) because of the coordinate singularity at the event horizon (time slows to a stop). There is even a book called Frozen Star by Greenstein from the 1980s if you are interested in the history of this.
The reason what the article of this thread says may cause controversy or confusion is because of the cultural way the resolution of the original issue got converted into a "talking point"/recurring example/"de-confused". In free falling coordinates, crossing the event horizon is no more special than walking across Earth's North Pole. There is no "problematic" infinity until the actual center point (which is what the Hawking-Penrose singularity theorem is about, but that theorem in essence assumes non-evaporation). That theorem itself was in response to speculation of some process intervening to "bounce" collapsing stars and censor black holes from the universe.
All these statements are fine and still correct as far as they go, but one has to be careful about the background assumptions embedded in analyzing things in free fall coordinates. A long history of poo-poo'ing the coordinate singularity or some hypothesized bounce process as "unreal" or "unphysical" led to a tradition of always analyzing things in free fall coordinates (as the arXiv paper in the OP does!). The validity of this transform does have implicit requirements, just not in the pure math of the general relativity transforms but in the physical context. E.g., it requires an infinite background future (i.e. no Big Crunch) which seems to be implied by data these days but was in great doubt for decades. It also assumes a non-evaporating situation which has been in doubt since the mid-1970s with Hawking Radiation.
Here's the important point which I cannot emphasize enough: WHAT ACTUALLY TRANSPIRES IS REFERENCE-FRAME INDEPENDENT. At some (maybe far) future time, a mass concentration is either there or it isn't. Period. Reference frames change observed rates/the clocks/positions maybe but not the actual core situation. If a distant, non-freefalling observer can see a Black Hole evaporate to nothing in a finite-time, then at the end of the day [ or the hole
People have been speculating about micro-black holes evaporating into nothing ever since Hawking's initial result. In that light there is no news younger than 40 years old here.
To be sure there are some specific dynamics to be modeled here and what this paper does is model them in free fall coordinates. All those details are surely important to pro physicists. The zinger headline of non-formation doesn't rely on such details. It only relies upon any mass-energy transfer from within the hole to a great distance away and enough time in the heat death to have evaporation be the dominant process (or else a small enough black hole that it doesn't need much time). Hawking Radiation is but one such process, though a theoretical one. Most think (on similar general theoretical grounds) that any quantum gravity will have ways for strong gravitational fields to decay. So, it seems likely that there will be some process, but sure, sure, evidence is needed, too.
Logically, though, reference frame independence of what actually happens means that any argument against non-formation is translatable to an argument against Black Hole decay. Contrapositively, any argument for black hole decay is an argument for only incomplete black hole formation. There may be possible glitches in last-moment of existence type stuff, but that truly is blind-leading-the-blind territory. I actually tried to raise this in 1988 with my freshman relativity professor but I don't think he understood my point and he mostly poo'poo'd about how Hawking Radiation would break down at the last moment of decay or something.