Except that diesel turns to jello below 40*F unless you get the much thinner winter blend which will hold out to -10*F per the local co-op's sign. If you don't leave it in gear at night all winter you won't get it in gear until spring and even then you are probably going to stall it out.
It has wax in it to lube the itty bitty parts in an injection pump, nothing like the gears in a transmission. It is also the wax that gells and turns it to goop which is why the drier winter stuff doesn't have as much (but still some)
We use diesel for flush in tractor/geardrive combine transmissions when somebody splatters something to get the filings out because it is a little better and far cheaper than parts solvent and any residual will mix with the 15+gal of gear oil much better than water (which is murder on any clutch/brake linings) Yes people do actually try to use water...
The parents JD F525 lawn mower shares the engine oil with the hydrostat trans, I think it is a really stupid setup but it just calls for John Deere 10-30 turf-gard oil.
I plan to run ATF per Ford in mine if I ever get one. They tested the thing and warrentied the thing with it, can't be too bad.