First of all, the ES9016 has much better specs than the 9010 found in the A-S801. Based on AH measurements, the A-S801 has approx. 1 dB higher output, two channel driven, 4 ohms, FBW than something like the AVR-X3300W. It has lower THD, but the Denon 3000 series are known to have THD+N so low that even dogs won't complain (borrowed that from Gene
). The Denon AVR-X4200W, X4300H (I bet X4400H too toon) had been as low as $799 brand new, those would beat (practically same) the A-S801 in 1,2 channel driven into 4 ohms.
Very true, but you can get a pocket size external usb dac headphone amp for $100-$200, even with the same ES9010K2M iirc+Macbook pro and done too with the AVR-X3300W. That's an added piece, but you gain portability and usability (listen to hifi sound with smartphone/headphone). With a D&M AVR, you also gain Audyssey XT32 with SubEQHT, more manual EQ options, streaming, direct play from USB thumb drive. That's just a few useful features even for 2 channel applications, aside from the obvious advantage on the video side and many other convenience features.
Everyone may have good reasons to go for a 2 channel integrated amp, I did too just last year when that little NAD was on sale for less than C$500/US$400 and for my desktop speakers there was no room for an AVR. The A-S801 is quite good if you can get a brand new one for $750 ($899.95 Amazon price). If it fits my need I would not hesitate to get one either but I would not expect it to sound any better than a Denon 3000 or Marantz 6000 series, especially after you shared the schematics/service manual. So depending on an OP's need and the way the questions are asked, I wouldn't always bring up the integrated vs AVR thing.