I like your idea of working these things out statistically but by your phrasing it's not necessarily what's being done (as in there are no reliable enough numbers for odds that matter).
But even if those odds were available, no matter what patient chooses, once you tell then there is a positive result, the fact that false positive is possible and odds are not in favor of treatment so they make a choice to do nothing does not mean they get to live a normal life from now on. Patients are not pure bayesian choice machines. The choice you make will affect you in big unknown ways and the existence of such choice already affects you until your EOL and has repercussions. That cancer was detected in your body cannot be "unheard" or "unread" back. Maybe you manage to deal with it, maybe you will live in constant stress. and of course chronic stress is connected to tissue inflammation, sleep disruption and other issues.
Therefore your argument that screening is automatically good does not seem to be convincing to me