Maybe in Britain, but in the US, it’s almost always the driver on the right who is required to yield when traffic is converging.
Basically, the two yield requirements are independent of each other; the left turn yield is dependent on the north-south traffic, and the right turn yield is dependent on the east-west traffic. The driver turning left from the southbound street is effectively eastbound traffic when the merge happens, so the northbound-to-eastbound right-turn driver is required to yield.
If you offset the intersections, it becomes easier to understand. Instead of making the intersection a crossroad, move the southbound lanes west by 500 feet, so the northbound and southbound lanes make two independent T intersections with the east/west road. Now you can see how the person who makes the left turn from the southbound road is part of the eastbound traffic when he gets to the northbound intersection, and you can see why the person making the right turn from the northbound lane has a yield requirement.
By moving south bound west, you totally change the dynamic.
4-way stop, driver on your RIGHT has right - of - way, not left.
The right turn driver is traveling south, requiring the northbound driver to yield.
South bound takes right turn lane, clears north bound to make a left turn.
Now, both are going west. But, who is turning into what lane?
Left turning into far lane, illegal.
Right turning into far lane, illegal.
Both are in correct lane, nothing happens. One or both are illegal.
Without being there, it's all armchair quarterbacks and mostly pointless.
Other than show the complexities of allowing turns without a dedicated green.