Once I’ve made something, WeVee keeps hold of it – I can’t download it or put it on other video services like YouTube, etc (although you can embed clips elsewhere)

I expect there’s a technical reason for this. The Flash plug-in makes it reasonably easy to stitch together video clips into a sequence, but to then export that as a single video file in its own right would require a lot of heavy server-side tech, which is not all that compatible with the flash stuff. Not impossible, but a lot of work.