Empty blocks minimise your stale shares.
Why would you prioritize stale share rate over publishing a useful solved block? I fail to see how pushing an empty block through provides any worth to the Bitcoin network.
If the purpose of having blocks is to record transactions, and the purpose of having a blockchain is to have a record of those transaction, why send an empty block? What purpose does it serve? What benefit to the network does it provide? Why does the solver deserve 25
BTC for an empty block? Does this have a false impact on difficulty adjustment since the block is solved so quickly, yet has no value (other than to the solver)?
Every block provides security for the bitcoin network, one of the main purposes of mining. It buries the previous blocks under another block making it that much more difficult for a malicious miner to revert the chain (hence the 6 confirmation general rule).
The "empty" block is worth just as much to the network as any other block. It would be better for the block to be found, add that security, than to waste miner's resources spinning their wheels on stale work.
The whole "empty block" nonsense is just nonsense. It happens pretty rarely (less than 1% of our blocks) and when it does I'm sure the miners appreciate having been able to solve a fast block rather than a stale, and users of the bitcoin network appreciate their transactions gaining an additional confirmation.
It's worth pointing out that this is not something unique to Eligius, either.