However, given that cancer cells do not evolve between individuals (as opposed to bacteria and virii), if we are to find a efficient immunological treatment it's going to stay efficient. If anything, we will evolve for our cancers to respond better to it.

Well, until you deal with super cancer.

https://en.wikipedia.org/wiki/Devil_facial_tumour_disease

Wow, that's an actual transmissible cancer, not a transmissible trigger.

Somehow it is strange that cancer cells do not try to propage to other organisms, given they try hard to invade their host? Is there any known reason for that (absence of) behavior?

See Retric's comment and link. Short answer is, can.

A more common transmission mechanism is itself a virus (https://en.wikipedia.org/wiki/Oncovirus) .

But, remember unlike bacteria or a virus, cancer isn't typically "invading" and you aren't "hosting". It's a malfunction of your own cells resulting in unregulated growth. For the most part it isn't really something you "get", so much as a failure mode of you as a system.

We do use the terminology "invasive" but not because it came from outside the body, rather that it is leaving one organ or tissue and entering another.

Well, it's because it's not "cancer cells" as something different then the host, it's just "here's some cells that, for whatever reason, decided to start growing and multiplying indefinitely, rather then being restricted by what their programming says". Comparatively, cancer is far "less threat" then most diseases, except for the fact that your immune system treats it like part of your body. Thanks to that "leg up", it can do a lot of damage. If your cancer got into another person, their immune system would treat it as foreign (modulo transplant factors and such), and attack and destroy it.

They do https://en.wikipedia.org/wiki/Clonally_transmissible_cancer

I imagine a big part of it is that they kill the host pretty quickly.

Although they may evolve from parent to child, so what works for one generation may be less effective on following ones.

Only if dormant cancer cells get passed from cured parent to child, which generally should not happen.