Except.. there are a lot of iridium layers in the geologic record. These things tend to happen every 10-20m years. The most recent is probably the Eltanin impact about 2.5m years ago. The K-T impacter is definitely one of the largest, but not by as much of a margin as you might think. The mere presence of an impact within a million years or so of the mass extinction is neither surprising nor damning evidence, and Alvarez never bothered to make the case beyond that.
And if you look at the history of mass extinctions, most of them are triggered by climate changes from geologic events. Pretty much every time there's massive vulcanism, most of the species on Earth die out. And hey, what do you know, there was a truly epic scale volcanic eruption going on for millions of years right at the same time! What a coincidence.
The Chicxulub impact is certainly part of the story of the extinction event that killed off the dinosaurs. But the evidence isn't there to assert that it is the whole, or even the most important part of the story.
Alvarez looked at the global iridium layer 66M years ago and said "This is from an impact. I don't know where the crater is, but there is one and when we find it, it will be X km big and date to 66M years ago." Then the Chicxulub crater was found and matched his predictions to a T. That is a hell of an impressive scientific accomplishment. Which may or may not have anything to do with the K-T extinction event and the end of the dinosaurs.
To your question, my understanding is that if you ignore the K-T asteroid impact and look at the fossil record up to but not including the iridium layer, it looks very similar to the P-T die off. Same early indicators, same die-off patterns (e.g. starting with single celled marine organisms, changeup of specialized niche species, acidification, ecosystem collapse, more fungi etc.) Then of course the impact happened and reshaped everything. BUT, the argument goes, the impact had such drastic effects on Earth life because basically all the existing ecosystem slack had been taken up by the downstream effects of the Deccan Trap eruptions.
IMHO the researchers like Gerta Keller who push the Deccan Trap only theory are mainly butthurt about Alvarez. But if I were to steelman their position, it is that a P-T like extinction event was already clearly underway, and if the asteroid impact hadn't happened we would have seen basically the same die off over a slightly longer period (or if the impact had happened without the Deccan Trap eruptions, there'd have been enough resilience that maybe the impact wouldn't have caused extinctions?), and so we should assign causality to the volcanos. Hard to prove a hypothetical though, which is why I think the one-two punch explanation is better science.
Edit to add: checking Wikipedia, I see that chemists Frank Asaro and Helen Michel are also credited as part of the core team, although it still gets called the "Alvarez hypothesis".
Eh, that's underselling Luis Alvarez a bit. He wasn't just "a physicist," he was a Nobel laureate and arguably one of the twentieth century's few Renaissance men. My favorite Alvarez hack was when he used muon imaging to 'X-ray' the Great Pyramid. He didn't find any hidden chambers, but later researchers did.
In the Alvarez mass-extinction hypothesis, he simply followed where the evidence led, unlike the supposed professionals in the field.