Cancer immunotherapy is a whole field of research and treatment, yes.

I assume the immune system probably already reacts to this in a specific way. For example, a major bruise has a lot of broken up cells, but doesn't warrant a big immune response.

Major damage tends to cause a much larger immune response than a vaccination. That said, they do have therapeutic cancer vaccines that present proteins from cancer (sometimes patient-specific) with adjuvants to help stimulate the immune response.

There were reports that if you inject the goo from melting the tumor into another mouse, that mouse became much more resistant to that class of tumor[1], so...

[1] - https://news.engin.umich.edu/2023/10/these-bubbles-kill-canc...

First issue is that tumors don't necessarily have to be highly immunogenic, e.g. there're tumors that don't present many neoantigens on the surface. This means immune cells can't easily recognize them. Second issue is that tumor microenvironment evolves to be immunosuppressive. There're many different signals that regulate immune cells activation and simply having antigen-specific cells isn't enough. But as someone said in a sister thread, what you're describing is a basis for multiple clinical trials that combine antigen release with immune activation.

Exactly my thought.