As the quality and the number of cameras radically increased in the last decades, the quality and the number of UFO videos didn't increase.

The only exception I saw were the videos released by the government agencies, they are actually interesting.

Basically, the prevalence of smartphones means we can record pretty much anything at anytime. Therefore, if abductions happen with any regularity, surely at least one would be captured on camera.

My understanding of that statement is that, with the advent of ubiquitous smart phones with cameras, there's not much room to believe someone's claim of alien abduction these days. If they have no picture or video to prove it then it's likely not true. Sure, some people may get abducted without their phone, but the possibility of no one ever having a phone to record such an event is statistically improbable.

So, with too few people able to suspend belief and buy into claims of alien abduction without proof from their phone, no one really makes that claim anymore.

Maybe that's not what the GP was getting at but that's how I read it...