I'm taking this a little out of order.
But that last point is the cornerstone of the invasion/migration hypothesis.
I find that rather ridiculous, as well as an arbitrary and unreasonable condition placed upon the concept of migration. If the starting point is A and the endpoint is C, there's no good reason to insist a migrating population couldn't stop over at point B in between. In Philistine terms, I see something like a stopover on Cyprus as a plausible scenario. Indeed, Cyprus could potentially have served as a sort of gateway to the Near East, considering its pre-existing commercial links across the region and, in particular, its apparent cultural ties to the Aegean region.
Perhaps "descended" was a poor choice of term because 20th century caucasian Amercians "descended" largely from Europe, but there was no invasion nor mass migration.
In my view, that's complete nonsense. The USA has a population numbering in the hundreds of millions and nearly every single member of this population descended from the many millions of people who came here from far-off places. In actuality, much of that immigration came in concentrated waves of mass migration from certain foreign countries and regions during particular periods of our history. As for whether it amounted to an invasion, I'm sure there were many Native Americans who thought so. There've been quite a few nativists who weren't too happy with all these foreigners entering our country either.
It is widely known Aegeans spread themselves across the east Aegean all through the 2nd millennium, this was not an invasion nor a migration.
You are correct that we have evidence indicating migration was common throughout this region over the 2nd millennium BC. We clearly see evidence of it in the archaeology as well as written sources from the region like the corpus of Hittite treaties and diplomatic correspondence. However, generally speaking, those phenomena don't appear to be anywhere near the same scale as the movement of the Philistines into the coastal Levant. Previously, we have evidence of things like merchant and artisan communities among a myriad of other smaller and more isolated groups from all over which settled amongst a sea of the existing population surrounding them. When something like a community of Aegean artisans or merchants came to Egypt or a Levantine polity, it certainly doesn't appear they arrived in sufficient numbers to impose their own material culture and practices over that of the locals. This doesn't appear to have happened with immigrants of apparent Indo-Aryan descent either. While it's obvious in many cases that cross-pollination occurred and there may have been significant changes in terms of politics or warfare (e.g. the apparent situation of Mitanni, Egypt under the Hyksos), the existing cultural paradigm generally persisted. Hence, I simply don't see this prior evidence of migration as analogous to that of the Philistine example. If the Philistines were primarily composed of these prior assimilated groups I would expect the existing culture to have remained predominant rather than see sudden and broad cultural change.
If the DNA suggests these 'Philistines' came from Europe within say a generation then you have evidence of possible migration, if it only suggests they came from Europe over a timespan measured in hundreds of years then the invasion/migration hypothesis falters.
Actually, their evidence says quite the opposite, that this migration was not something that occurred "over a timespan measured in hundreds of years". In fact, they found discontinuity between the Bronze and early Iron Age populations of Ashkelon. The early Iron Age population strongly featured European ancestry while the Bronze Age population did not. That's how they concluded this was the result of an influx of new people during the Bronze-Iron transition period. The signal they detected was strong but relatively short-lived...and completely absorbed into the regional population within 200 years. Interestingly, the Philistines were powerful enough to entrench their political and cultural paradigm so deeply over the area that it appears to have actually survived far longer than their genetic profile. Obviously, this necessarily implies a significant migration event occurred and then came to a halt as the Philistines subjugated and mixed with the existing local population rather than being sustained by a long period of additional migration. The paper can't quantify an exact number of years over which this migration occurred but, realistically, their findings do necessarily limit its duration to a relatively brief period. And certainly, "hundreds of years" seems far outside the realm of possibility.
Indeed, which makes the initial claim (...It now appears rather difficult for objective thinkers to continue to claim there is "no evidence of a mass migration") somewhat meaningless. There is still no clear evidence of a mass migration.
The evidence appears as clear as a bell to me. I would go so far as to assert that, when combined with the archaeological and very small epigraphic corpus, it all gels together and looks rather conclusive. Again, I would note that those who think this was purely a local phenomenon believe it, not because there's any concrete evidence to support that interpretation, but only because they think it's merely possible and prefer not to consider whether a far-flung migration occurred. I realize many probably find this an unwelcome development which challenges cherished sacred cows but here we have substantial empirical evidence of a far-flung migration which clearly refutes the local event hypothesis when it comes to the Philistines.
So what really, does this DNA actually tell us?
There's nothing earth-shattering about it. On a fundamental level, it merely verifies empirically a conclusion many have independently drawn from the archaeology alone. What it doesn't tell us is much about the broader context of the Sea People or the associated conflicts engendered by this agitation.
I don't recall anyone suggesting the Philistines were ethnic pure bread Semites.
Why would they?
Though if they have lived in some part of the Levant for several centuries (around Alalakh & northern Syria?), but originating from the west in the mid 2nd millennium, this sounds to be consistent with the DNA analysis (not having read it), so how does this support the migration/invasion hypothesis?
As noted above, this is not consistent with the researchers' findings, nor does it seem consistent with earlier records concerning migration in the region that I'm aware of. In particular, the Hittite corpus covers the topic of migration in this area. While there are certainly extant records concerning a people around this area who could also be a Philistine group or related group, they were contemporaries of the Philistines occupying the southern Levant, not a Philistine power base which existed earlier in the Bronze Age.