Sharing the pull-down will cause problems with cables that have an IC and need power. These cables have a pull-down internally, Ra = ~1kΩ, on the CC pin that is not being used for the CC wire. You can see it in this diagram, probably from 2:
Imagine what happens when Ra is present if both CC pins are tied together on the UFP and connected through a single Rd to ground. The DFP will see the combined pull-down of about 830Ω through both Rd (5.1k) and Ra (1k) in parallel on both CC pins.
It will appear to the UFP that it should supply VCONN on both CC pins and that there is no DFP connected. A charger that doesn't support USB-PD, i.e. 5V only, might not bother to care, but a USB-PD charger will likely refuse to supply power.
Also consider the UFP's problems. Of course you can't sense cable orientation, but for only power and USB2 that doesn't matter.
The UFP will sense 0.07V on CC for a 56kΩ Rp (500mA supply) or 0.38V for a 10kΩ Rp (3A supply). If the UFP is trying to do USB-C power supply sensing, it should detect the first as below the 0.25V threshold and consider no DFP connected, and sense the 2nd as a 500mA supply.
All that said, if the UFP does not care about orientation, does not try to draw over 500 mA and so does not try to sense DFP power capability, and one does not use a cable with Ra (e.g. a 5A charge cable), then there isn't a problem.