The difference between SpaceX stopping its launches to figure out why the booster was damaged on landing is substantially different from FAA grounding the entire fleet. FAA observing the SpaceX process and making the determination that it was inadequate, if they have a reason to believe that, would be a much less intrusive middle ground. Involving a bureaucratic decision is always going to be a time cost. The issue is whether the FAA really needs to be in the driver's seat for everything that doesn't work 100% perfectly at SpaceX. SpaceX had to push on the launch license for its StarShip tests to exclude some things from FAA's "mishap" declarations when the tests did not go 100% perfectly but obviously did not put any people at more risk than what the permit actually envisioned.
This failed Falcon 9 landing occurred on a barge in an area where SpaceX had already determined that the weather was not good enough to launch the Polaris Dawn flight because an abort of that launch would have required recovery of the crew capsule in the same weather. So, the problem may have been in the judgement of SpaceX about what weather parameters were needed for barge landings. And, considering that it was the 23rd launch of this booster, maybe SpaceX was thinking to push the envelope with that particular piece of equipment, although I would think it better to keep that one going to see what wears out first with more launches.
Bureaucratic regulatory agencies always claim objectivity, but my experience in working at one is that the claim is not always true. There is almost always a tug-of-war between boosters and skeptics inside such agencies.
I have not worked at or with the FAA, but, from the outside, I am left to wonder how the agency permitted Boeing to launch StarLiner with its inadequate resolution of the thruster problems it had on its previous flight, but calls a "mishap" when SpaceX sends an uncrewed test rocket on a mostly successful test flight that shows real progress in developing the spacecraft and did not exhibit any failures that were not anticipated as possibilities before launch.