"that charity probably has someone running a similar algorithm"

That does not follow, unless you're assuming a community of perfect rationalists.

I'm assuming here a community of average people, where Reporter Sara happened to run a personal piece about her favorite charity, Honest Bob's Second Hand Charity, which pulls in $50K/year. The story goes viral, and suddenly Honest Bob has a million dollars in donations, no clue how to best put it to use, and a genuine conviction that his charity is truly the best one out there.

Even if we assume a community of rational donators, that doesn't mean the charity is itself rational. If the charity won't rationally handle over-saturation (over-confidence in it's own abilities, lack of knowledge about other charities, overhead of distributing, social repercussions, etc., etc.), then the community has to handle it. The ideal would probably be a meta-organization: Honest Bob can only really handle $50K more, so everyone donates $100, $50K goes to Honest Bob, and then the rest is split proportionally and refunded or invested in to second-pick charities.

However, the meta-organization is just running the same splitting algorithm on a larger scale. You could just as easily have everyone donate $5 instead of $100, and Honest Bob now has his $50K without the overhead expenses of such a meta-organization.

So, unless you're dealing with a Perfectly Rational charity that can both recognize and respond to it's own over-saturation point, splitting is still a rational tactic.