There's no good reason a DAC can't be part of an integrated box.
Technically speaking, you can get superb measured performance from separates that beats any of the integrated boxes you listed for around the same price (e.g. Topping D90SE + LA90, $1800). The only issue with the Topping amp is its relatively low output power - 90 W @ 1% THD into 4 ohms. You didn't mention what speakers you were going to use, so it may not provide enough juice at the volume you want to listen to.
Do you already have a streamer? The Hegel seems to be the only one where you can stream from your phone using UPnP. That would really simplify things, if it's the direction you intend to go. Currently, I use a RPi 3 B+ with moOde for streaming duty.
Hope this helps.