The app itself lets you "revoke" a pledge i.e. double spending it back to yourself. That's pretty fundamental to the whole model and is why money doesn't get stuck if a project never makes it to the finishing line. It also keeps it low risk for the pledgor - if they suddenly need the money for some reason it's always available to them.

Without SIGHASH_ANYONECANPAY Lighthouse would still be possible, just with a much worse UX. Basically you'd have to inform the project owner of which output you wanted to use, and then once enough value was pledged, the owner would have to construct a transaction with everyones pledges in it and then pass it around for everyone to sign. It'd be a two step process - very ugly. With the malleability features it's "fire and forget", much easier.