There can be kind of a two prong "test" to determine if screening is harmful. Physically, is it a good idea? Answer is probably no. We're not in a scarcity situation really where the "prestige" demographic isn't getting recommended to get appropriate tests based on their risk factors (on the other hand, some of our poorest aren't getting them but that's not an issue solved here). The other side is mentally. Again, I'd argue that people with a clean unnecessary screening got out lucky. They'd be mentally much worse off had something come back positive.
Bizarrely, there's new data suggesting that even fixing known problems, like coronary artery blockages doesn't improve mortality in a lot of situations you'd think it would. That suggests that we're doing too much screening in that case (I mean, if the treatment is worse than the disease... why screen?), not too little. As another example there is a well-known vascular surgery group going to churches under the pretense of "screening" for leg atherosclerosis, then performing high-margin, high-turnover, and unnecessary procedures on the very high "induced" false-positives.
I also find it utterly bizarre that screening would include lung capacity testing. In an otherwise healthy adult who can say, climb a flight of stairs or something of the sort without getting shortness-of-breath, that test is completely meaningless and expensive from a "disease" perspective. On the other hand, it does give you a number to compare to your peer group, kind of like resting heart rate. On the other hand, resting heart rate is free, can be done yourself, and literally takes 15 seconds to measure.
In the end, I'm not really against having these sort of "prestige" medical services available. Particularly because more choice is generally good-- and it's your body, you should do what you want with it (within reasonable bounds). But, everyone should educate themselves because on balance, I doubt people end up up feeling or being better off considering the ones who will have false positives.