Yeah, but that’s like saying that your muscles are working all the time, not just when you are exercising. It doesn’t change the fact that exercise is a direct stimulus that improves overall performance.
I think vaccines do the same thing to the immune system. They “stress” it, but within controlled parameters. The result is a stronger, more resilient ability to fight off all diseases, not just those specifically targeted by the vaccine.
Here’s another example:
Study finds COVID-19 mRNA vaccine sparks immune response to fight cancer - UF Health .