Yes, but that's not a problem with screening as a concept, that's a problem with those screening methods. We accept "destructive testing" in medical screening (e.g. biopsies; x-ray fluroscopy with both radiation and carcinogenic chemical tracers; etc.) because we haven't structured medical screening in such a way as to incentivize investment into "non-destructive testing."

The medical establishment doesn't care about the potential for harm from repeated use of methods on patients†, precisely because we think of them as things that only need to be done rarely. There's been no need to optimize for "low cumulative impact" in screening methods, because there's currently no incentive to do screening often enough for it to matter.

Let me put it this way: the state of the art in MRI technology (reducing required size + cost per machine to enable more frequent + "trivial" use) is being pushed forward economically almost entirely by demand from Operations Research in the aerospace industry, rather than by demand from hospitals wanting to have more MRI-machine capacity per patient. That's ridiculous.

† The freshest example of this on my own mind isn't diagnostic per se. Have you ever noticed that dentists don't tell you to close your eyes — nor give you UV-blocking wraparound goggles — despite shining a UV light directly at your face for 30 seconds at a time to harden UV bonding resin they've used? They know it'll hurt their eyes if they stare at it all day — which is why the UV lights they use have circles of UV-blocking backscatter guards, to allow them to look at your face without reflected UV light hitting their eyes. But there's no concern for what they're doing to you, because you're only getting a few cumulative minutes of concentrated dental UV per year, vs. their cumulative hours of exposure.