You can't take a "standard" .rpm from the Fedora repositories and install it on CentOS. You can't take a .deb from Debian 11 and install it on Debian 10.
If you're using a "Debian based" distribution, the "standard" .deb is the one shipping with Debian. If it doesn't work on the derivative distro, they are doing something wrong. Or like I said, maybe the dependencies are doing something wrong.
This is the problem that Flapak, Snap etc try and solve. I won't put AppImage onto that list because it actually doesn't solve the problem it just makes it worse.
I was under the impression that Debian already solved that problem by allowing you to deploy an older Debian version in a chroot with debootstrap? As long as the Linux kernel is binary compatible, that should work fine. Although I have to admit I don't use stale software that often, so I have little experience in that area.
I mean, you can, if you also install its dependencies. And you may end up with a weird franken-system, but you can. You can even automate it and set preferred distros with pinning, it's how people run things like hybrid testing-unstable distros.
Oh, not all libraries support that. They need to...
You will very likely bump into conflicts. Or you you need to upgrade a lot of fundational libraries (like libc), at which point why stay on Debian 10?
Backports exist for a reason.
Backports do indeed exist for a reason, I just felt like challenging “can’t”
https://refspecs.linuxfoundation.org/lsb.shtml
These are, of course, not distro packages, but ISV packages and most RPM features cannot be used.
The irony here is that we’re discussing flatpak/snap, which take the idea of static linking to the absolute extreme by doing something closer to a container where every dependency is part of the package. Maybe static linking being “against distro policy” is tossing the baby with the bath water by causing maintainers to reach to a much worse packaging method (snap) because the distro policy is just too obnoxious.
There’s no good reason you couldn’t just statically link (or relocatably copy) your dependencies into your .deb except the distro maintainers being purists. It would make the process of building a deb (or RPM or whatever) trivial because you’re using it as a dumb archive format for your build artifacts, similar to how a container works.