Cost, simplicity and reparability.
Adding gears to an automatic is straight-forward, basically add planetary gearsets until you're happy with the number of gears.
The hard part is gear selection. Four speeds is the largest reasonable number of gears that can be managed "automatically" without computers. Generalizing here, but with a four speed, you can control gear selection using just two solenoids.
- Gear Sol A Sol B
- First on off
- Second off off
- Third off on
- Fourth on on
Then you can wire up these two solenoids to simple logic circuits so that they activate when certain conditions are met. Tie SolA to engine vacuum & RPM, and SolB to vehicle speed and you'd have an effective, if rudimentary, mechanical transmission controller. As an added bonus, if any of these solenoids fail, then the transmission will be stuck in second gear, which is usually short enough to take off from a dead stop, while tall enough to maintain reasonable enough speeds to limp home.
When more gears are added, this kind of mechanical shift logic becomes unfeasible. Not just because of logic complexity, but it's difficult to obtain the kind of data the transmission needs to properly select a gear without sensors to detect things like throttle position. Thus, the industry waited until computers were pretty well established before moving beyond 4 speed automatics.
Ditto for things like CVTs. It's totally possible to build a functional planetary CVT using 1940s tech, it will just be a "manual" CVT with a lever the driver would use to control engine RPM (think: thrust lever on an aircraft).
In addition, 4 gears in a conventional automatic is more than it sounds like. Anyone who has driven a 4-speed manual can tell you that the gear spacing is pretty wide, and it's definitely a compromised driving experience. A 4-speed automatic is much better than that; it kinda/sorta acts like it's somewhere between five and six gears thanks to the operation of the lock-up torque converter.
You start out in first, with the torque converter slipping quite a lot. That's terribly inefficient in terms of sending power through, but it does have the effect of multiplying torque as much as 2.5 times to help you set off. So you've got something that looks like a granny gear below first. You'll notice that 4-speed autos tend to have a surprisingly steep first gear, and this is why they can get away with it.
As vehicle speed increases, the torque converter slips less, and you get gears 1 through 4 with the engine only spinning a little bit faster than the transmission. If you watch the tachometer while you add throttle, you can see that the engine speed starts to ramp up before the car's speed due to a small amount of remaining slip.
Once you get to a steady state in top gear, for instance cruising down the highway, the torque converter locks. A little clutch in the middle of the converter binds the input and output together and prevents slip. If you're cruising one of these cars and just feather the throttle, you'll notice that the tach and speedometer are synchronized, but if you push harder you'll get what feels like a small downshift as the torque converter unlocks.
There's a big efficiency benefit to having the engine speed rigidly locked to the car's speed, but like the shift logic for 5+ gears, that's relatively hard to do without computer assistance. Modern transmissions are likely to lock the torque converter up in every gear and give the same kind of connected feeling of a manual transmission, only letting the converter slip to set off from a stop and to shift gears. But the old 4-speeds with their simple logic generally only gave you that lock-up in 4th gear cruise.
Thus, 4AT is just about fine in a rudimentary vehicle like Jimny. Maybe not in more complex vehicles, but it's a Jimny.