I’d be cautious about doing what you’re doing long term. I think you’d be better off learning to let go of stressful thoughts before bed, and to make your bedroom a very calm, peaceful, non work related place where all you do is rest and relax. Watching old tv shows before bed, or while on a timer that will turn off when you’re asleep, sounds like a good way to get you relaxed, but I don’t think it’s great to have that type of stimulation continue during sleep.
I’ve done the same thing you’re describing during high stress periods with podcasts, and while it’s better than letting worries keep you up, I find myself feeling more “shallow” and less insightful/less rested if they stay on throughout the night. When I allow myself to relax and drift off without distraction, I find myself feeling much more “full” and “together” in the mornings, particularly if I take the time to go over and record my dreams.
It has been about 6 months of doing this all night, every night. So far, I feel myself.
The key is to use old familiar programs. Things you can visualize even though you're just listening to them. It's that familiarity that allows your brain to have a sense of comfort, while not really being stimulated.
In any case, the experiment continues...
That way you can get more REM sleep, while still not waking up due to lack of background noise.
I recently had a lot of trouble sleeping due to stress and found a solution whereby I began listening to old TV shows while I sleep with earphones in bed.
It was miraculous. But one odd side effect is that I don't really dream anymore - at least not in the same way. Since the shows are playing, it's almost like they are dreaming for me.
If the phone stops playing the shows for some reason, I'll have dreams again - and often wake up due to some annoying thoughts about work.
I haven't noticed any negative effects. Certainly there was a massive positive benefit of just being able to sleep when I couldn't before.
... but these sorts of things should be avenues of research.