I think BB is too beloved to just simply be written of. Especially with his death involving a gigantic televised explosion.
Well, by written off, I don't necessarily mean ignored, as if he never existed. But I don't think he'd be able to function as a character on the show anymore, mostly for the reason you cite in your second sentence.
It's announced that BB is going into the Challenger. A lot of kids probably watch him waddling onto the shuttle with the other astronauts. Then, bang, the Shuttle explodes. Even if parents try to shield their kids from the reality, everyone else is going to be talking about it, and not always with genteel solemnity, for a the next month or so.
So where does PBS go from there? I guess they could try for a repeat of of Mr. Hooper's death, though that ultimately was about an old man dying off-screen of natural causes, almost certainly an easier "sell" than a character who is essentially a child himself getting incinerated on international television.
One thing I could see resulting from all this would be a backlash against "crossover" appearances by characters geared at children. Producers might not want to run the risk of having other beloved icons meet a tragic end in full view of the public. Even stuff like appearances in Ice Capades might be eyed with some trepidation(eg. what if the rink collapses and Snoopy gets crushed?) Not that all such appearances would halt, but the people who make these decisions might be a lot more careful about licensing and stuff.