The actual reason you really need a proper PID 1 is not explained in this post, but a couple of clicks away at [0]:
>[...] the init process must also wait for child processes to terminate,
>before terminating itself.
>If the init process terminates prematurely then all children are terminated uncleanly by the kernel.
It also needs to reap orphan processes or they will become zombies. The dumb-init code does not appear to be doing that so I reported an issue[1].
In general docker is half-trying to be the init system, but most people using it are putting a whole child os with its own init system in their container. I think the approach that rkt uses where it uses systemd to run the process is safer. Now if people would just start using lightweight containers...
Considering phusion/baseimage has been around for more than 2 years and plenty of people have been using an init system inside their containers that contain multiple process, why didn't Yelp just pick something up off the shelf? Why not use runit or one of the plenty of more mature lightweight init systems?
I can't speak to the others that have been mentioned in this thread (tini in particular seems to be identical), but the solution used by phusion/baseimage is written in python[0] - a C-based solution allows for lighter-weight containers
