That and I mean, what are we going to do with the hay afterwards?
Well I'm not saying that it is a foolproof method, but it also isn't as complicated as you think it is. Hay isn't a very rare substance, so plenty of it can be found quite easily. It's also easier to clear hay out of the water than oil and it's still more effective than Corexit.
I think that the oil eating microbes featured in the first video would be a lot more effective though.