The ONLY problem I have had with this, is the controller on the system itself defaults as controller 1, so SOME games it takes a little fiddling to use different controllers. But I have done this and it works great.
I've used a handful of different USB to HDMI docks, and I haven't had any problems with any of them. I just use an anker dock that supports gigabit ethernet, 100W power passthrough, and HDMI, and it works just fine.
https://www.amazon.com/gp/product/B087QZVQJX/
You can use just about any controllers using Bluetooth, I really like the wireless XBox controllers (only supported over Bluetooth) for this. But I've also used the Switch controllers and they work fine.
It's really just a slightly expensive setup for what it is, but it's also very portable, so...