This makes sense for a material currency, where you wouldn't want to be burdened with useless paper rectangles or metal coins. (Same thing for an embassy, by the way, which has a non-zero cost.) But for donations with a digital currency, I think it was reasonable to hope that they could just publish a Bitcoin address just in case without endorsing it for real, because the cost to receive Bitcoin is essentially zero. (Keep in mind that you don't even need to run the software anymore, you just need to keep a copy of the private key somewhere.)
This being said, the EFF's choice is cautious, but sensible. (It's just slightly annoying to see Bitcoin labeled as a "product or service", whereas it's supposed to be a protocol.)
The overhead of keeping BTC is probably low, but what happens if they lose that private key? How many people have access to it, what's the protocol for using it, ....? I know if someone sent me some BTC there's a good chance they'd be lost to the world forever.
And then people will throw a hissy if you aren't "using" their donation. Maybe their choice of the faucet can be viewed in a different light. They are using the donations to promote and ensure a bright future for bitcoin by spreading the wealth. :)
This being said, the EFF's choice is cautious, but sensible. (It's just slightly annoying to see Bitcoin labeled as a "product or service", whereas it's supposed to be a protocol.)