Why the facination with integrated amps?

The answer to your question is in the way its asked. All your pros are technical considerations, nothing about sound quality. Then the cons are also all technical, except for "long term subjective listening" which the giveaway there is "subjective". Nobody says "subjective" except to be derogatory, further adding to the obvious bias.

You like the technical stuff, be proud and open and honest about being a technophile. Own it. Just don't try and kid a kidder. I've shopped and compared and lived with both integrateds and separates long enough to know that if all you care about is sound quality for value you simply cannot touch a good integrated with separates for anything resembling the same amount of money.

The future is in one box wonders with dac, room correction, DSP functions, streaming, pre and amp all in one box.  Short signal paths and built in synergy are huge upsides.  Advances in DSP, Class D and digital are bringing a whole new world of lightweight  and terrific sounding gear.  Separates are not the future and sales will continue to decline. That pretty much sums it up in a couple of sentences. 

Space, total outlay, and complexity are big one's for me. I mean, think about it, the ideal bit of stereo kit is a unit the size of a paperback romance that does everything via a remote tablet or phone.

Add in an integrated with a good digital or phonograph section, and the question really is why would anyone insist on separates?

There's also a lot to be said for how and when we cycle through gear. I mean, if you are a serial audio buyer, then integrateds may not be your thing.

One of the important benefits of an integrated by the way may be reduced circuits. Your switching and volume control no longer need to be as complicated or built for all possible options of amplifier. You can design this with fewer parts and more certainty that one is going to match with the other. Not to mention the potential for noise and ground loops introduced by going out of the pre and into the amplifier.

Grannyring; short signal paths is the equivalent of “unfiltered’” in wine. It sounds like a great idea in theory but in pactice there is little corrollary between it and long-term satisfaction. ‘Built in synergy”? Other than input/output impedence and gain, things that are easily checked for, there is no reason to think such an argument is valid. I could as validly argue the buyer of an integrated has less ability to “season the flavor” by mixing and matching. Class D? I don’t need to go into the sonic deficits of Class D do I? 

It's nice to have options.  I have separates in my main system.  I have more space and am more concerned about sound quality in the main system. 

I have an integrated in my home office (Audio Research VSi55).  I have a tuner, turntable, and DAC connected to it.  Volume is usually pretty low and it's mostly background music (either the tuner or Spotify or Tidal through the DAC) but if it's a slow day or a late night of work, I will crank it up every once in a while.  I have a pair of Klipsch Heresy I speakers with a bunch of Bob Crites upgrades and the sound quality is very pleasing those times I do crank it up.

In my computer room I have a Heed Elixir integrated and a turntable, DAC, and Sony headphone amp.  I have some space limitations in that room.  The Heed doesn't take up much space and will drive my Canton speakers louder than I can listen to them.  The sound quality is excellent and the headphone amp in the Heed, while not as refined as the Sony is excellent.  It also has a phono pre, I haven't tried it yet, but by all accounts it's quite good.

I also have a Peachtree Nova 300 which has a great amp, dac, and phono preamp.  Quite frankly it has more bells and whistles than I need and it is currently for sale (replaced by the Heed).

The integrateds I own meet (or exceeded) my needs and were affordable options for the space and use I bought them for.  While not as good as my main system, if something happened and I had to downsize, I'd be really happy with either one of the systems I've built around my integrateds.