I doubt we have cancerous cells throughout our lives.
We have defective cells throughout our lives, and the immune system appears to play a role in removing such cells (though processes like apoptosis and DNA repair seem to play a much more crucial role), but that’s not the same thing.
Of course, some infections increase the chance of developing certain cancers e.g. Genital warts -> cervical cancer, so the immune system can help you here if it can prevent you getting infected.
The immune system also attempts to fight tumours, but I don’t think there is data to say a strong immune system = better chance of spontaneous remission.
Interestingly, there is some evidence to suggest that acquiring a feverish infection may promote remission, because it triggers processes that can affect the tumour. Cite (pdf)
So perhaps it’s best to have a mediocre immune system, that lets you get sick but then is strong enough to mop up the tumour as well as the virus