Online videos are lossily compressed. If you record them, either you do so losslessly (which will be huge) or you recompress them and lose quality. Plus you have to deal with network buffering, notifications, alarms, etc., not to mention having to wait while you're recording.

If you can download the source video, it's a lot easier.

I agree, but sometimes some videos are not easy to download, in that case it would be helpful to have a means to do an "accelerated, off-screen recording"