A4LD was used from 1985 to 2012, almost 30 years, so not a bad transmissions as automatics go
It was renamed 4R44E(1995) and then 5R44E(2001), but mechanically it never changed, the valve body was changed to use solenoids.
And the A4LD was itself a C3 automatic with OD added, C3 was first used in 1974
So the base transmission has been around 38 years, and no matter what you may think of car makers they are in business to make money, and a "bad transmission" is bad for business, so they would have dropped the C3 or A4LD if it had high failure rate, not added to it.
Incomplete or poor rebuilds got them a "bad rap" from trans shops that had never seen an OD automatic in the early years, so they screwed up and then blamed the design, as all humans like to do, lol.
The early ones did have there growing pains, like all new technology does, but if properly rebuilt with the newer parts A4LD should last 200+k miles
Good read here on A4LD:
https://therangerstation.com/tech_library/a4ld.shtml
Not familiar with Temp dummy light?
All automatics run on fluid pressure, not a Ford thing, usually transmission problems is a loss of pressure
The torque converter is bolted to the crank, via flexplate
The outside shaft of torque converter that slides into the transmission drives the transmission's main pump(front pump), this pump provides the 125-175psi ATF pressure needed to engage clutches and bands(brakes) in the transmission
So no or low pressure = no go
Could be pump itself or several seals or gaskets have failed over time, so enough pressure has been lost
Reverse requires the highest pressure to engage, over 160psi, so when there is a pressure issue its usually seen first as slow to engage reverse, or no reverse
Slipping "gears" can also mean lower pressure
There are pressure test ports on all automatics, but they would be useful only to pin point possible internal leak points, but with 0 engagement I doubt it would be helpful
Its possible the flexplate has broken but usually there would be a noise with engine running
Check the fluid level with engine off, should be over full
Then check it with engine running, should drop down to between full and low lines
If level is not changing then pump is not working