An x-ray still damages your dna, guaranteed, and your cells then have to repair it. The older you are, the harder that is to do, and the more times your cells have to repair dna, the more you age [David Sinclair's theory of aging anyways]
I don't think you will find a health practitioner who would think that's safe for 1 year, let alone decades of doing it.
1,000 chest X-rays per year would be 60 mSv -- which is over the 50 limit for nuclear employees. A chest x-ray isn't really comparable to an hour spent on a commercial flight: it's sixty times as much radiation.
Let's drop the nuclear worker max as if it should bear on normal folks: Well known doctors like Peter Attia, Rhonda Patricks, and others I've heard on podcasts recommend max 5 mSv per year as limit that risks health and accelerating aging.
Another ref, look at the FAA's data where they measure exposure on different flights: https://www.faa.gov/data_research/research/med_humanfacs/oam...
e.g. NYC to Tokyo averages 22 microSV per hour. A chest x-ray is 20 miscroSV.
Importantly - each year simple, normal living exposes you to 3.5 mSv (see the same chart), so you only get 1.5 mSv to "allocate" to other exposures.
In other words you only get 75 chest x-rays per year.
By FAA rates of exposure on trans-pacific flights, you should take max 5-6 of those legs per year.
[0]: https://en.wikipedia.org/wiki/Orders_of_magnitude_(radiation...