I think the J85 was an important part of the F-5 success. Being a glorified supersonic trainer with only the minimum of its customers needs. J85 is simple and cheep. I’m not sure how many contemporary single engines are.
I'd be hesitant to say as such since twin engines implies doubled maintenance work hours. No one had trouble operating massive quantities of F-104s or A-4 Skyhawks, after all, which had big engines of similar vintage. The J85 was probably just chosen because physically small engines were crummy back then and F-5 was a combatized form of T-38. Less the engine and more the plane picked.
F-5 was supersonic unlike the Skyhawk, and lacked the expensive radars and long range combat capability of the F-104, thus neatly fitting into a nice "day fighter" role that could do more than lug Bullpups around. Like intercept bombers.
The J52 was another good option as I think the T-38 itself competed with a Super Saber-based trainer, and the J52 was cheap enough to be disposable much like the J85, but I don't think the J52 actually existed at the time. But a J52 powered jet would be very different from the F-5 in layout. It might actually fit in a Super Saber though, or a supersonic Skyhawk.
J52 and J57 would both provide similar power to the F-5 over the dual J85 setup, which is all it really needs to do. They're also pretty cheap (enough that Argentina and Israel, both very poor countries at the time, had quite a few them) and J52 would be common with Skyhawk.
Maybe Israel would get super F-5 instead of Mirages who knows.