I think it really depends how well they make the characters merge into whatever's going on, funny or serious. If a character can still play into the current dynamic and feel like they fit, they can work. If they just spend each and every appearance doing the same old skit with no alterations of course they'll feel like dead weight. I mean Team Rocket's butting into every plot post-OS really has a "When are they going to get to the fireworks factory?" feel, they're not contributing to the dynamic, they're just doing their own thing and cutting the new ideas off rather than complementing and flowing into them. Hell the show itself treats them as irrelevant nuisances, but at the same time doesn't do anything with that. Ironically the OS was the only time the twerps really had a funny chemistry with them regarding it so they don't really click together as a fun rivalry otherwise. Brock meanwhile was famous for ending up a background character due to never altering his shtick of pervert gags or having many developed chemistries with the new companions.I think comedic characters like Misty/Brock/TR all worked best in Kanto when the show was a pure comedy. Johto was a bit half and half because while the show was still mostly humor based a lot of the filler plots started to get really dull. It's obvious that much like Ash, Misty/Brock/TR aren't meant to get much character development when they're on the cast outside certain episodes, so they were designed to last as long as possible till the writers started changing the show.
If you think about it much like Ash/TR get resets now every gen, the same was starting to happen with Misty and Brock only they just got stagnant instead. Since every other companion just has a limited timeframe of 3-4 years on the show before they leave, the writers likely know what they're going to do with them. Of course they still mishandle things like Serena should have gotten more focus, the SM cast isn't always balanced, etc....but those are the breaks since the anime staff aren't exactly brilliant writers.
I guess the trick with Ash is that they often alter his character slightly to fit with the new dynamic and characters, so he usually still immerses into the rest of the series. Others like Brock, Misty and TR didn't really get fine tuned to keep standing out as the formula changed (besides maybe TR in BW, though many agree that was maybe too drastic).
This is the most likely reason for some new characters that just don't 'click' either, the writers didn't think through how they would fit into the series' premise, usually they just have a few running gags and a goal and run that into the ground.