|You know it makes sense|
During the second season of Star Trek TNG, Dr Crusher (played by Gates McFadden) was replaced by Dr Pulaski (played by Diana Muldaur). The balance of fan opinion seems to be against Dr Pulaski (indeed, some fans seem to positively dislike her). However, my view is that she was much the better of the two characters.
I should say at the outset that this is no reflection on Gates McFadden, who is an excellent actor and made the most of the character. It's about the two characters.
One of the important things about Dr Pulaski is that she develops. It has been said that there was a plan for her to be McCoy to Data's Spock, but if so it didn't work out like that. When she arrives on the Enterprise, she has difficulty accepting Data as a real person. In "Where Silence Has Lease" (TNG) she refers to Data and "it" before correcting herself, and as "non-living" before again correcting herself and noting his official status. In "Elementary, My Dear Data" she argues that Data can never have the intuitive understanding that comes from experience. But as time goes on she comes to appreciate him. In "Peak Performance", almost at the end of her time on board, Data loses a game of Strategema to an (organic) opponent, and removes himself from duty until he can work out what has gone wrong with him. Troi and then Pulaski try to talk him out of it. But listen to Pulaski, when Data starts explaining what he is doing: "You may be able to sell Troi that story, but not me. You're smarting because you were beaten." By now she is the one insisting that Data is capable of human character, and accusing him of using his mechanical nature as a cover for it. Data isn't persuaded, but Dr Pulaski has come a long way.
This is important because in general the characters either simply accept Data (most of the crew) or refuse to accept him as alive (the scientist who wants to dismantle him, etc.) In "Measure of a Man" Data wins the argument. But Dr Pulaski changes.
Another of Dr Pulaski's merits is her lack of deference to Captain Picard, in contrast to almost everyone else. In "Peak Performance", again, Troi and Pulaski eventually go to Captain Picard to get him to intervene. Picard complains that "I have to hand-hold an android." "The burdens of command," murmurs Pulaski, unimpressed. She's witty, she's been around, she's seen it all.
There are several occasions in the course of TNG where Captain Picard is behaving very oddly, even putting the ship at risk, due to being taken over by aliens or whatever. I'm sure we've all been there. In "Time Squared", when the Captain becomes deeply unsettled by the arrival of his own future self (who is unable to communicate) Dr Pulaski tells Troi that her duty is to the ship first, and that if she sees signs of irrationality, she will use her authority to relieve him of command. It doesn't quite come to that, but you know she would. Dr Crusher, by contrast, lets oddly-behaving Picard go on and on. In "Lonely Among Us", she tries to get possessed-Picard to undergo tests, he threatens to call security, and she goes away meekly. Of course, if she didn't let Picard go on and on, there would be no story. The only time Picard actually does get relieved it's by Riker ("Allegiance"). But Dr Pulaski is a much stronger character. In the film "First Contact" Picard refuses to blow up the ship to destroy the Borg. It's obviously irrational, as Worf points out. You can see that Dr Crusher agrees, but she just says "Once the Captain has made up his mind the discussion is over." Katherine Pulaski would have relieved him of command at that point.
And look at her relationship with Worf. When Worf gets an embarrassing childhood disease, Dr Pulaski treats him but gives Picard a cover story which preserves her patient's dignity ("Up the Long Ladder"). These things matter to Klingons. Worf shows his appreciation by performing the Klingon tea ceremony for her—and she takes an antidote so that she can take part (the poisonous tea is normally fatal to humans). When does Dr Crusher drink poisonous tea with her patients? Perhaps there is a sort of affinity between Dr Pulaski and Worf, which might have developed.
Loking on the Internet to see what other people think, I found that many people refer to some of the same things I have. But in the case of the anti-Pulaski faction, some of the same things that I like are seen as negatives.
There's a very good video about Dr Pulaski (song: "Grace Kelly", with the refrain "Why don't you like me?") at https://www.youtube.com/watch?v=zn7DNeupi3M (that was the link last time I looked, anyway)
As I said, Gates McFadden does a great job with the character, despite the material she was sometimes given. (Remember the sex ghost in "Sub Rosa"? Many of us have repressed the memory.) I have a special fondness for the episode "Remember Me", which is heavily focussed on Dr Crusher.
By the way, Diana Muldaur had appeared twice, as different characters, in Star Trek TOS. Both are very memorable episodes.