Well, sure, you can do quick little gags like that. Bart's blackboard gag can be topical (as with the recent, heartbreaking "We'll really miss you, Mrs. K" message); Huey Freeman can sit in front of an (unseen) news report about Al Sharpton complaining about last week's episode. My point is that you can't write an entire episode around a recent event.
Simpsons lampshaded this rather nicely in one of my favorite gags, in the Super Bowl ep where the names of the teams are very, very obviously dubbed in after the original recording -- and then, this being during the height of the Clinton impeachment proceedings, they also dub in "President -- CLINTON -- and his wife, -- HILLARY".
(Also, per my copy of the Beavis and Butt-Head movie script, the reason that Chelsea Clinton is folding laundry when Butt-Head goes into her room is that the movie came out right after the 1996 election and, had Dole won, we would have seen a wider shot of her packing her bags.)
But as I said, writing and animating an entire episode that's as timely as the South Park Schiavo episode is just impossible for a bigger-budget network show.
Related: I just read a Legends Revealed about the
'Nsync episode, which includes this paragraph:
The episode, which has a U.S. Navy officer secretly forming a boy band around Bart and his friends as an attempt to brainwash kids into wanting to join the Navy, has gained a bit of a bad reputation in the years since its release as helping to popularize a specific type of Simpsons episode that has become more and more prevalent over the last decade plus, which is an episode that seems to be geared around the celebrity guest stars in the episode more than anything else. The episode itself, though, is quite good.
I'm inclined to agree. Modern Simpsons doesn't just date itself in terms of political references, it seems really interested in playing with flavor-of-the-month stuff like currently-popular celebrities and the latest gee-whiz Apple gadget.
I think the major difference between, say, New Kids on the Blecch and the Lady Gaga episode from a year or two back is that the show isn't actually built around the 'Nsync cameo; you could take them out of it and the episode would still stand on its own. That's not the case with the Lady Gaga episode; if you took her out you wouldn't have an episode.
It's not that there weren't early Simpsons episodes where the plot WAS written around their guest stars -- Stark Raving Dad and Homer at the Bat are both absolute classics, and their guest stars really WERE essential to their appeal. (And both, oddly enough, were in season 3.) But I don't think they're quite the same as what the show does with its celebrity guests now. For starters, Michael Jackson playing a mental patient who thinks he's Michael Jackson is a stroke of fucking genius. And as for the softball team, while it's a who's-who of early-'90's all-stars, it's more about them being all-stars than about the episode being specific to WHICH all-stars were in it. You could rewrite the thing with current players and it would still work, with all the ridiculous made-up traits and all (Strawberry as kiss-ass, Scioscia just wanting to do an honest day's work, Boggs having very strong opinions about who was England's greatest prime minister). They also seemed a lot fewer and farther-between. Guest stars playing themselves has been the norm in recent years, while in the old days they'd play one-off characters (Dustin Hoffman as Mr. Bergstrom, Danny DeVito as Herb Powell, Beverly D'angelo as Lurleen Lumpkin, etc. -- when someone like Adam West or Leonard Nimoy showed up to play himself, it was usually a quick cameo, not a central role in the episode).
I think they've started swinging back toward the guest-stars-as-unique-characters idea; last year's use of Tom Waits as the leader of the survivalist group is a good example. And Neil Gaiman's appearance in the previous season's heist episode is an example of a guest star used absolutely perfectly -- a role that serves as the punchline of the episode and says something ridiculous about the celebrity, but mostly involves him staying out of the way while the plot works itself out.