Best Integrated, period.

With the same proviso, no such thing as best, I suspect the Vac Phi beta would be best in most circumstaces. Meaning it's output of 110 watts I believe, would drive most speakers. Having had a few very good integrated amps, Lavardin IT, Karan K180, clearly the best in my system was the Viva Solista. At 22watts, clearly, it won't be best in many systems.
Others I might mention, the newish Pass labs 150 integrated and Conrad johnson C200. Not much experience of them, but the companies products are always good, in my view

Symphonic line Kraftwerk mk2, they make great amps.
Blue Note Demidoff Diamond, never heard it but it should be interesting.

I prefer when a integrated is a onebox solution otherwise it looses its appeal a bit, a least to me. Therefore the ASR with 3 extra boxes is out of the question.
Heres another: Consensus Audio Amp 211.
The Vac Phi Beta is definately interesting, still wonder about the others and how they compare.

The Blue Note seems to be the most expensive one so far at €19990.

It depends on the speakers being driven...