It could have been administrative, but I always felt the implication was that Crusher was as exceptional as the rest of them, because everyone on the Enterprise was supposed to be the best of the best and that's a note they hit regularly. I'd always thought it was implied that they came to Crusher for that post because she is one of the absolute best doctors in Starfleet, but after a year she realized that kind of job wasn't a fit for her and she was happier out in the field and with her son.
But they aren't explicit about any of that on screen, and the viewer really can fill it in different ways. The writers decision to explain all this coming & going by papering it over with a line and then moving on does leave quite a bit of room for interpretation.
After "The Child", is Bev mentioned at all in season 2? Had Pulaski stuck, I wonder if Bev would have remained as forgotten a character as Pulaski ultimately was.
Well, certainly they gave the impression of wanting to leave behind any of the missteps. Tasha too is barely spoken of in season 2. Is she mentioned anywhere but Measure of a Man? It isn't until subsequent seasons that they warmed up to embracing the entire history they had been through. I actually wish that shift could've included some mentions or reappearances of Pulaski. It really was the one missed opportunity to tie things all together imho
You're right that there's very little to judge it from, just a few offhand remarks about Pulaski & even less about Crusher's reputation, but the fact that she did go to Starfleet Medical & then left & had her spot waiting for her on the Enterprise just as easily, whatever the circumstances, does tend to speak on its own, as to her station
I'm not saying there's any reason to think of Bev as any less a top doc than Riker is a first officer, or Picard is a captain. It's true they wanted us to see them all as being the best of the best, but for some reason, they explicitly engendered Pulaski with a noteworthiness they never imparted on Bev, before nor after. Pulaski's acclaim seemed almost like fame, whereas Bev's came off more like status, the kind of doc who could come and go on the flagship, or take up the top spot at Starfleet Medical, & leave it behind just as easily. It just smacks of someone who has pull
I just remember that one time Bev had something of a defensive attitude about Pulaski's memory erasing technique, in Who Watches The Watchers. It just, once again, made Pulaski seem like some kind of famous hotshot in the medical community, and while I imagine the reason they felt obliged to talking up their new doc in season 2 was because of the need to compensated for a cast change, ("Hey this new doc is really good too!") that one remark about her, after Pulaski had gone, was still kind of rubbing it in on poor Bev lol