It’s not so much that it doesn’t support the Exec bindings but that the Exec binding isn’t all that useful.
The whole purpose of a container is to provide everything that a single program needs to run in one package. In some ways, you can look at a container as a wholly separately running operating system.
But, the container also only includes just what the program running inside it needs to run. There are no extras available, like Python. Some containers don’t even have bash. So most of the things you will want to have access from the Exec binding won’t be there. And even if stuff like Python were there, it will be limited in what it can do outside of the container.
Personally, I run everything in containers. It makes installation, upgrade, and backup pretty simple. I don’t have to worry about incompatibilities with libraries or ports or the like.
Or outsource that stuff to some other app you can command more indirectly such as through MQTT.
With one exception (Calibre which doesn’t offer an official Docker container) I always use the “official” images from the software provider unchanged.
You might look into Ansible. I have all of this (minus NodeRed) running in containers installed and managed by Ansible playbooks.
If they have the option to install this software not in a container you will probably have better performance. Converting media streams tend to be RAM and CPU intensive and containers do increase the amount of RAM needed to run a set of software.
On a Pi1 that could make a real difference.