It's just conjecture as to why the UL design was never adopted by AM transmitter manufacturers. I'd guess the cost of a special modulation tranny with tertiary screen windings was outrageous.
I use a Williamson with a pair of 6L6GCs to drive my class B modulators where the grids of the 304s really 'swing' into conduction.
In my junk box I have a driver transformer from a BC-5P transmitter that used 4 x 6550 in push pull parallel in UL mode. The transformer has screen and plate taps on the primary.
The driver output drove a couple big triodes (3x2500's?) in class B.
It's interesting that you had success using UL in a driver.
I figure my transformer would work well with 6L6's or 6bg6's instead of the expensive 6550s.
So UL was used in the broadcast industry at the speech amp/driver level.