It's not that 1020 or 1025 isn't heat treat-able...in fact it is...1500-1600 degrees and water quenched...it just doesnt get much for the effort, as you state correctly, 4130 annealled is overkill, strength-wise. Really, you are Carburizing the 1020(adding Carbon) whereas for 4130 you have quite a few selections of what you'd like to heat treat to, for the physicals you wanted.
The point is you'd have a ton of warpage if you heated an entire fuselage to 1550 and dunked it...which would never make sense and wasn't at all necessary when you gas welded 1020. The Pre-Heat, Weld and stress relieve (post heat) was all done, one cluster at a time. One worker with a cherry bomb for pre and post heat and another doing the actual welding. 4130 is mostly the same. post heating is cheap insurance to slow the bead shrinkage by cooling it more slowly.
Pretty efficient back then.
I believe they did away with 1020 simply for the fact that the steel mills quit producing in the thin walls and 4130 is still produced in thin wall tubing today, so it was just a simple, stability of supply issue.