I'll throw my hat into the allways on debate.
Personally I don't, and that's largely because I was initially advised against it, but with hindsight I honestly would never get the time to edit a video from the reels and reels of footage shot. On an average 1 week trip I can easily still end up with 3-4 hours of footage, which if I'm lucky I can make a 20-30min video out of. Even being selective still gives you lots of junk!
If your housing does not allow you to access controls then you obviously have to leave it running, but if you do have controls then the other thing to consider is that if you do a 60 min dive then you've used a tape up. That means you have to open up your housing reload and reseal. That's never a good thing to do in a dive environment and can lead to all kinds of fogging situations and even floods. One more thing is that I bet normally if you don't have time to turn your camera onto record for something, then the overall shot wouldn't have been that great anyways. There are of course always exceptions to this!!
In the end people will find what works best for them. No one does everything exactly the same, you can only get advice and work out what's best for you.
RICoder was initially asking a few questions about colour and shakiness on the end video. These are discussions all of themselves, but there are a few pointers. With colour then if you have access to white balance you need to do this frequently, some would advise before every shot, but at least on every depth change. If you are still not happy with the end result then you can adjust colour with editing software after the dive. Most NLE editing systems will have some colour correction tools. It's hard to get it perfect, but with practise it's possible to get something that you're happy with.
As for shakiness then moving over from photos you have to remember one thing in particular. A photo is a split second capture while a video is taking 10 or more frames in the same amount of time. You have to have great buoyancy control to get a good end result and even then you'll still end up with stuff that looks like you're in a washing machine! Don't give up though - diving with a camcorder will make you more concious of your buoyancy and movements in the water - as a result you'll become an even better diver and as a result of that you'll shoot better video. It's a win win situation!
Ok I've rambled on enough now!
Cheers, Simon