Each script is a bunch of boilerplate that has to reimplement the same stuff.
So shared libraries don't exist? That hasn't been a problem in a long time on BSD or OpenRC systems. Seriously, it's not hard to factor out code into a library. If you're only considering Debian, you have to remember that they are always behind (sometimes FAR behind) the update cycle.
The functionality is inconsistent between services.
Again, only if you were a moron and reinvented the wheel each script instead of using a common library.
That said, the ability to do things different is very important when you need to support something unusual.
To check whether a service is running, it uses pid files.
No, there is not requirement to use PID files. That is simply a common way to implement a daemon. With sysvinit and sysvrc (or OpenRc), this kind of thing is an implementation detail that is out of scope.
It doesn't have useful logging.
Again, this is by design, as it left logging *unspecified*. If you don't like syslog, nothing was preventing you from using something else. (also, "useful" is subjective)
because init doesn't log service crashes.
Patently incorrect, as I have used syslog to inspect startup crashes many times over the last *twenty years* I've been using UNIX. Maybe this has been a problem for other people, but I've never seen it. If your syslog is configured badly, that's an entirely separate problem.
While I can't speak for all distributions (you seem to have had some history with poorly-configured environments), there is nothing wrong with using sleep based polling. The only reliable way to detect if a prerequisite service is ready is by directly polling the service. (e..g issue an HTTP GET to a web server) The timeout is to allow startup to proceed in case of an error, (so you don't end up bricked, unable to use your computer)
There is a reason most distributions stopped using super-servers like xinetd: on-demand startup isn't that useful. Start your service at boot. You can defer expensive tasks until the first requests, if you want, which is when you would pay that cost anyway in an "on demand" launch. Listen to on the port, block on accept(2) or select(2) or similar, and let the OS page you out to the swap partition.
"On demand" isn't necessary, because the kernel already provides that feature. Adding a redundant implementation simply increases complexity and adds more opportunity for bugs. Super-servers make it even worse, as they add the risk that a problem in on service could take down all the services provided by the super-server.
Breaks horribly the moment something goes wrong.
Ok, now you're just trolling.
Want to have some fun? On a systemd box, pretend you just installed some updates, and you need to restart a few daemons so they run the updated versions. Try restarting dbus (system, not user). (You might want to make sure any open files are saved first)
Also, you might want to actually read about UNIX before you make these kinds of accusations. Reading taoup is a good place to start.