Pulaski should've been the first Emergency Medical Hologram, actually. Everything would've been solved. Everyone would've been happy and Kate Pulaski would've been able to continue on in TNG for years and years to come. Instead, Diane was brought into someone else's gig as a scab and this was handled in a way that seemed to represent the uncertainty everyone had about the whole situation, to begin with.
The idea that Kate and Riker's father got it on offered some story potential, but went nowhere, when it was really the only aspect of her character that could've afforded her any affection. Being an Ice Queen works best - and perhaps only - on hot, young women. Kate should've been afforded much more warmth, if she were to be a part of the crew. Instead, she comes off as snotty to Wil, telling him to get over his crappy childhood. So, now ... her only "IN" with this crew went bye-bye. Now, they've got no reason to want to hang with her and yet they just can't seem to shake this crotchety old interloper. She's like a hanger-on, with everybody looking at eachother After Hours saying, "... who invited her?"