Essentially I have the solution you desired to set out to achieve, just through lucky choice of base hardware - single cable from desktop/laptop to dock which carries two monitors, keyboard, mouse, audio and network.
This stemmed from a hatred of USB-C Docks - I was provided a low end mac laptop for work and a usb-c dock with a DisplayLink chipset in it to drive two monitors on my desk. This was so lacking in performance there was visible lag on the desktop as the dual core processor was completely swamped having to render 2x1080p displays entirely in software. Basic tasks were unacceptably slow, the machine was demonstrably faster on battery than it was plugged into this dock and receiving power. I self funded a Caldigit TS3+ dock and immediately could use the laptop as it should have been in the first place, we got immediate approval to expense a purchase of these for the whole team. and I brought my dock home.
I have a HP Workstation as my desktop and the official method for supporting Thunderbolt 3 is exactly as you describe, install the add in card, use the two short DisplayPort Cables to the DP Inputs on the Thunderbolt card, and to then use the single cable to connect to the dock. GPU Display Out -> Thunderbolt PCI-E -> Dock. This appears to be the scenario for all desktop PCs using Thunderbolt, even the computers with the chipset built into the board - there's always a DisplayPort Input involved to present the display output from the GPU to the target.
On the counter side to this even Apple who are all in on Thunderbolt have problems with this separation between Display and PCI-E - If you look at the Mac Pro they've done some serious work with their custom PCI-Express implementation in the form of their MPX extensions to enable Thunderbolt support through their GPUs, by the looks of things they do the opposite thing - essentially routing PCI-E through the GPU and out of the USB-C ports on the GPU.
As an aside - nVidia discontinued USB-C Ports on their GPUs with the next generation 3000 series, this I think will lead to less confusion going forward