You still have no way of operating the GUI elements. Phones have a touchscreen interface.
When the phone is in "pretend to be a desktop" mode, with a Bluetooth keyboard and an external monitor, its touch surface would behave like a trackpad. People who have used Apple's Magic Trackpad would have little trouble adapting.
And in carrying all those bits, you might as well have brought a laptop
I didn't carry a monitor. I carried a phone, a ZAGGkeys Flex keyboard, and an HDMI video cable, and I'm using someone else's monitor that happens to be in front of me.