Good question. I'm 90% sure that fallback function is actually implemented in byte code by comparing the byte code against all the method signatures. Then if none match, the assembly jumps to the fallback. So, what you save in 0s in the input byte code, you pay more than that in the execution gas.

Yeah, for gas tokens you're right. This was all pre-Flashbots, so talking about February or March at the latest. Flashbots kind of wrecked the whole game. Now it's a whole lot simpler, just ship transactions to Flashbots and bid as close as possible to breakeven. Consequently 90%+ of the profits now go to the miners.