Why the facination with integrated amps?

OP we could not possibly disagree more. Oh well, it is the nature of these threads. Noise, noise, noise and noise again.  If you think short signal paths mean nothing, then I cannot help you. You asked why integrated gear is hot and you now need to be open minded about the reasons and possibilities. Carry on. 

Best sound I have ever had is with my Lyngdorf 2170 one box wonder.  I still build tube amps for fun, but the 2170 with room correction and built in dac simply sounds better.  I mentioned some of the reasons above and they do in fact play a role.  The times they are a changing and broad brushed statements bemoaning digital or Class D etc... are just plan old short sighted.  The innovation pace of all things digital and music is very fast,  very fast indeed. The fun and exciting part is all this is leading to more and more one or two box solutions that use little energy, are light in weight and sound phenomenal. 

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.