Is there a “UAP phenomenon” worth studying?

Of your two takeaways, the second one strikes me as the more useful, because it's actually measurable. Camera resolution, sensor sensitivity and the number of devices in circulation have all improved by orders of magnitude since the 1950s, so if image quality of UAP reports has stayed flat over that period, that's a quantifiable trend rather than an impression. Has anyone tried to plot it?
There are a lot of variables that would make such studies very difficult.
A person with a fixed focus film camera with only 20 exposures on a roll of film is less likely to use up one exposure on a hard to distinguish blob in the sky than a person with a digital auto-focus camera that can store thousands of exposures is to click the shutter button.
So not only far more cameras today but far more likely that a person with a camera will try to capture an image. Thus lots of indistinguishable points of light captured today that might actually have been seen in the past but not photographed.

Perhaps more close-up saucer photos in the past than today, but many of the "good ones" were probably pie plates suspended from branches with string. Not so many close-up saucer photos today because they would be harder to fake? A study of what the UFOlogists say are the best photos of the past versus those of today?
 
There are a lot of variables that would make such studies very difficult.
A person with a fixed focus film camera with only 20 exposures on a roll of film is less likely to use up one exposure on a hard to distinguish blob in the sky than a person with a digital auto-focus camera that can store thousands of exposures is to click the shutter button.
So not only far more cameras today but far more likely that a person with a camera will try to capture an image. Thus lots of indistinguishable points of light captured today that might actually have been seen in the past but not photographed.

Perhaps more close-up saucer photos in the past than today, but many of the "good ones" were probably pie plates suspended from branches with string. Not so many close-up saucer photos today because they would be harder to fake? A study of what the UFOlogists say are the best photos of the past versus those of today?
The other interesting aspect is that has become clear that many mid-20th century reports were of stars or planets; people were culturally prompted to "watch the sky" and interpret distant spots of light as alien craft, like the infamous cases of police chasing Venus or Barney and Betty Hill thinking they were being chased by a blinking aircraft warning light.

And, of course, in the first few decades of aviation pilots were increasingly flying at altitudes and in conditions no one had ever flown through before at a time when, again, there were cultural prompts from science fiction and popular culture to interpret flocks of birds and atmospheric phenomena as potentially alien craft.

How this relates to the photographic evidence is that people are culturally prompted to take photos of things; a prominent UFO report would prompt people to look at the horizon and the night sky for UFOs and notice planets and stars, and some people would, you know, toss hubcaps in the air and take pictures of them to hoax sightings. The really obvious hoaxes and photos that wound up being of identifiable things get forgotten; only the vaguest images remain in the public sphere simply because of their ambiguity.
 
The other interesting aspect is that has become clear that many mid-20th century reports were of stars or planets; people were culturally prompted to "watch the sky"
There are also a lot more people now near cities where clear skies are often obscured by haze, and fewer out in the middle of nowhere, where skies can be clear enough to observe stars and planets. I have seen both the Milky Way and the northern lights, in mid summer in central Ohio. I've never seen such clear skies again, until we went out to visit an unpopulated national park in Utah.
 
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