How critical is dumb-init for Docker?
Something like dumb-init or tini can be used if you have a process that spawns new processes and you doesn't have good signal handlers implemented to catch child signals and stop your child if your process should be stopped etc.
If your process doesn't spawn new processes (e.g., Node.js) then this may not be necessary.
I guess that MongoDB, PostgreSQL, ... which may run child processes have good signal handlers implemented. Otherwise there would have been zombie processes and someone had filed an issue to fix this.
Only problem may be the official language images, like node, ruby, golang. They don't have dumb-init/tini in it as you normally don't need them. But it's up to the developer which may implement bad child execution code to either fix the signal handlers or use helper as PID 1.