That's the same with the Xbox controller though isn't it? Maybe it's different now but certainly when I was trying to get Xbox streaming working on my Surface Book last year I had to get the wireless dongle. I also had a hell of a time getting Xbox streaming working outside the house. Had to tinker with dozens of ports and NAT rules. At least the PS4 Remote Play feature works seamlessly, anywhere you have an internet connection. I think Microsoft's only really supporting game streaming to other devices within your own house. That said, I did get it working remotely :)
I really don't mind using the USB connected controller for PS4 remote play. I'm generally only using it on my laptop with a short cable anyway.