I don't think it is fair to characterize cosmology as not making progress no. Stuff is far away and occluded and hard to measure and see. Each improvement in observation causes a need to refine previous ideas, as expected. There are of course the two big mysteries that have lingered for a long time: Dark Matter and Dark Energy, but other areas of physics have lingering mysteries as well.
I almost had the same reaction, but technically they didn't say anything about cosmology not making progress. It's entirely reasonable to assume a scientifically minded person describing a field as "piling up question marks" means they think it's making a LOT of progress. Imagine a field that answers questions more often than it finds new ones; that'd be a pretty stagnant field to be in.
This is how I understood OP, too. Last time we had a "crisis in physics", it was the early transition from classical physics to quantum mechanics, when some good new ideas had been coinceived of, but trying to reconcile them with the classical way of thinking and with experimental evidence required increasingly convoluted hacks in the models to make it all work - until folks like Heisenberg, Born, Jordan and Dirac found more holistic and clean ways to approach the problem space.
The number of question marks piling up in cosmology does feel similar. It will help to shape new theories that reconcile all this experimental evidence.
Sometimes the questions keep piling up until someone happens up on just the right question. That question itself wouldn't have been thought of except for the thinking of all of the previous unanswered questions. Then the big Eureka!! moment and someone gets a Nobel prize 20 years later.
People dunk on cosmology because cosmologists have consistently, over decades, insisted, in public, that they knew more than they did, and are continually obliged to abandon what they insisted they knew. If they were more forthright about how much they don't know, they would get less criticism. They have much to learn from the biologists, who know they know practically nothing (even though massively more than you), and are happy to say so.
The health of a branch of science may be read from how eager its researchers are for you to know about what they have no clue about.
>cosmologists have consistently, over decades, insisted, in public, that they knew more than they did
Exactly, and each time the theories are proven wrong, it's explained as a never-ending series of "oddities", yet the theories are never altered in any meaningful way other than ad-hoc additions to explain each "oddity".
At some point there needs to be a reckoning that, for instance, the current theories of star formation are essentially completely wrong.
This is exactly what pushed me away from pursuing cosmology. One of the most important 'discoveries' in cosmology was that of cosmic inflation [1]. The issue is that if you model the big bang, what it creates is nothing like what we see. Regions of space that wouldn't have had time to have become causally connected (nothing could have gotten between them even traveling at the speed of light since the time of the big bang) are causally connected.
So the solution? There was some very specific period of acceleration, faster than light acceleration to some very specific degree, at some specific point right after the big bang which then ended at some other very specific point, at which point everything returns back to normal. What's the logic for it? Well if we do this, then what we see matches what we expect to see. It's an absolute retrofitting of numbers to make a model fit reality. And not only does that constitute good science in cosmology, it was sufficient to win a Nobel Prize.
It is literally unexplained magic being taken as a fundamental concept of science. And the worst part of it all is that it's completely unfalsifiable. We only have one universe to observe. So if it turns out that the discrepancy is actually being caused by many smaller effects we stand near 0 chance of ever discovering because each one of those small effects will have a million flaws, while the perfectly retrofitted inflation theory has "none." At worst they'll even get absorbed into the inflation theory model magic. Just add more epicycles!
It is one thing to identify a mechanism and show how in operation it must produce the numbers seen. It is entirely different to invent a name for a presumed mechanism, with no hint of how it happened to come to the numbers seen.