Why the facination with integrated amps?

For me it's bang-for-the-buck. I saved for 3 years to splurge on an Ayre AX-5. I'm not aware of separates at this price point that sound as good.

A separate amp and preamp has the flexibility that an integrated does not have!

Yes, but not everyone needs the flexibility and can be very happy with top end integrateds, especially if they bring nice tone controls along. :)

’Fascination’ looking for a reason... when you already have a position?

@grannyring is 100 percent correct in his prediction / assessment of the future, with respect to minimizing the number of components and offerings moving to all in one solutions.

In addition to the pros you listed, you can add one less power cord, one less isolation platform and perhaps even shelf if one is maximizing isolation. One less set of isolation devices, if one is going all in with isolation. One less outlet used in a power conditioner or a duplex in the wall. One less component to tweak, should one be into tweaking (and this one can add up, depending on the audiophile). Etc. AND this assumes a Preamp - Amp combination. Grannyring’s position saves at even higher levels.

Further, excepting the U.S. and a few other countries and the very wealthy (across the world) most people are living in smaller and smaller units that do not lend themselves to the footprint, cubic space, and cost that going with separates entails.

Since the vast majority (in billions, yes billions) are consuming music via a phone and earbuds or basic headphones...any investment by them will be made in inexpensive all in one devices, which they are already doing.

Integrated amps in the $$ upper end are at least as good if not better then seperates of even more money. My brothers 
Gryphon Diablo is a Perfect example of sheer excellence across the board , and with theoptional digital board really excellent 
and is a Best Buy ,for under $20k will go toe to to with Any amp,preamp digital at $30k  I heard many systems and owned a audio store in the UK for years . System synergy is key ,with 
great parts quality equal toor better the best modded equipment .
2 less power cords, and 2 less interconnects ,each seperate wire takes a pinch away  from the purest signal path. Myself bought 
a Gato 400-S with digital as well as custom analog build technologies from Denmark .i rewired it with VH audios best 
6-9s pure solid core Litz Teflon Wire. And top fuses for $6500
sounds  far more refined ,   There are very good  integrated amps but you need to do a lot of research and at least $5k and up if you truly want very good quality parts .  Everything is built to a certain 
cost parameter on average 25% goes into the cost that is why a $3k integrated has $750 in money’s spent including the case .
the latest  Gryphon Diablo was justbuilt with the best parts and Engineering - Period . By far one of the best integrated I  have heard , reviewers also agree .

Who cares. To each his own. Stupid topic.