Technically Final Cut does support native H.264 editing, through the open-format timeline feature. Technically, anything Quicktime can play back can be cut on a Final Cut timeline, with varying degrees of rendering required for real-time full-quality playback.
As you've discovered, it really doesn't work that way in practice.
The workflow you have is the objectively correct one: convert media in a non-conveniently-editable format into an intermediate format before cutting on it. The key question at this point is why it's taking you an unacceptably long time to batch-convert your H.264 media to ProRes. That's a relatively lightweight conversion process, as far as computer resources go, but it does require a significant amount of disk bandwidth to write out the ProRes media. Is it possible your conversion pipeline is I/O bound?
Since you're only going to Youtube, you might consider using DVCPRO HD as your intermediate format instead of ProRes, if ProRes requires more I/O bandwidth than your system can provide during the batch-conversion process.
Another option ? though I can't in good conscience recommend this one except as a what-the-hell experiment you might try ? is keeping all your media in H.264, but cutting it into a ProRes timeline. This workflow works very well for formats like DVCPRO HD and HDV, but I have no idea how it would work with H.264 media. Your system might not even be able to play back H.264 in a ProRes timeline in real time, which would be a total deal-breaker if it were me.