Yeah, I have to admit, I never really hated this series, and I too also enjoyed the "washing Brain's mouth" running gag. But I did find it rather strange that this series seemed to negate everything else from "Tiny Toon Adventures". And I often wonder why they did that. I mean, Kids' WB! was still showing "Tiny Toons" on weekday mornings at the time this show came about, so clearly the viewers wouldn't have easily forgotten about Elmyra's old co-stars like the writers apparently did.
Here's one easy theory I came up with to try to explain the changes: The last "Tiny Toons" production, the "Night Ghoulery" special, aired in 1995, three years before this. So maybe quite a bit of stuff happened to affect Elmyra's life between 1995 and 1998: 1) The other Tiny Toonsters complained enough about her, so Bugs had her transferred to Chuck Norris Grammar School; 2) Montana Max moved away, thus leaving Elmyra to pursue Rudy instead; and 3) Furrball and Byron ran away for good and Elmyra decided to just get new pets this time. And for whatever reason, Warner Bros. forgot to mention any of this to us. And they probably should have, seeing how they did just that for the changes between "Batman: The Animated Series" and "The New Batman Adventures" (in the form of the comic book mini-series "The Batman Adventures: The Lost Years").
However, I only just now noticed that the interior of Elmyra's house on "Pinky, Elmyra and the Brain" looks different than it did on "Tiny Toons". In fact, I just checked the TTA episodes "Hare Today, Gone Tomorrow" and "Take Elmyra, Please!", and I noticed that back there, Elmyra's bedroom was on the second story of the house, wheras here, it's on the first floor. So either that's another mistake that, unlike the ones mentioned above, can't be easily explained, or we'll have to go with this show just being a non-canonical spin-off set in some weird alternate universe where the other "Tiny Toons" characters (and the other "Animaniacs" characters, apparently) don't exist.