Thanks to Antonin Décimo.

Move custom video controls into its own function.  Remove some
DOM traversals, avoid querySelector.  Remove dead code.

Probably useless, but I'm supersticious.

We were inconsistent with stream creation.

It's not useful.

Users sometimes click on the button multiple times.

If a connetion is slow to get established, this would cause it to
be pushed twice, the first time before it is complete.  Thanks to
Roman Koval who noticed the issue.