> IMHO s6/daemontools and similar tools are just a helpers.
>
That is *exactly* what they are.


> They help to run as a unix daemon a program which is not written to be
> a unix daemon.
>
No, sorry, you are wrong. They are supervisors, and as such they ensure any
long-running job keeps running when it is supposed to.


> Now they pretend to the role of init, which they are not.
>
they can be, if you want them to. Some can do this better than others.


> And should not be.
>
lol, why not?



> The program should be modified to be able to switch to background
>
itself.

lol, why?

S6 even forces such a program must not handle daemon mode itself.

>     That process must not "background itself": being run by a
> supervision tree already makes it a "background" task.

>
You say this like it is a bad thing.