I asked a PSA why it's slow and she told me that when under manual operation the train is "off the grid", so to speak, and is speed limited for safety reasons (other trains no longer know where it is)
The door closing works well for the DLR -- the PSA checks all the doors are clear and then shuts them all at once. This probably isn't viable for a tube because platforms are smaller and more congested.
Just an anecdote: I use the DLR multiple times per day and after a few years using it I finally got stuck on a door the other day. I pushed the button to open the door, it started opening and when it was around 80% opened, I was entering the carriage, when it suddenly closed really fast. I got sandwiched on my shoulders and then on my right foot. The door didn't open, I had to force myself to remove the damn foot painfully. It did hurt. Can't imagine what could happen if it was someone weaker (like a child or an elderly). Oh, and my red snickers turned black.