I wholeheartedly oppose recycling of the same character between games that are not connected to each other.
By that I mean if MushA ran for a long time, closed, then opens as MUSH-A-PART2 where former players can continue their stories? I'm alright with that. To me it's no different than Firefly getting canceled and then the PCs are rebuilt for Serenity, the movie.
However, I tend to see a lot of weirdness and shenanigans in the wake of players who rebuild the same characters over and over again. Once someone tried to dupe me into remaking an IC romantic interest from 2 games ago. The players who do this tend to regurgitate story and attempt to get players to recreate the story elements that they want. There's also often little room for flexibility because the players who do this have something very specific in mind. In the end, there's very little surprise with recycled characters, and it's exhausting to me. Come on, be like the rest of the kids. Make something new. Have new experiences and put effort into it rather than replaying the same routine with the same character over and over again.
I make jokes about WoD players asking if they can bring "Their ________" (i.e. "My Tremere" or "My Get of Fenris") because it's a WARNING SIGN that you may also get slapped with an ubercharactercheese concept.
I have a RL friend that won't play Vampire: The Masquerade unless he gets to play His Gangrel, who is a 6th generation Gangrel with maxxed out stats, somewhere around 8 different maxxed out Disciplines (Wuuuut? A Gangrel with Fortitude, Auspex, Animalism, Potence, Celerity, Presence, Vicissitude, and Obfuscate? Ya don't say...).
So, in some cases recycled characters have less to do with a concept and more to do with recreating a character sheet of stuff some other staffer approved.
I just couldn't do it. For me? Fresh game equals fresh content.