Ultimately biplanes had 2 wings because the early state of the art in wing design was pitifully aerodynamically efficient. So it took a comparatively vast wing area to generate enough lift at the very low speeds the weak engines could push those very inefficient wings. Lots of vicious circles at work there.
Meantime, the structural strength of the wooden structures they knew how to build light enough would not support a long enough span to give the wing area needed to generate the needed lift.
Applying all this to roughly fighter-sized aircraft …
Said more simply, a biplane was a way to fold an e.g. 50 foot wingspan into two 25-foot wingspans that were strong and light enough to not fall apart under load while also generating 50 span-feet worth of lift.
They did this at the expense of needing a lot of external bracing, struts, etc., all of which created drag.
Once by the early 1930s we had learned to design more efficient wings that could carry the same weight with, e.g. a 35 foot span and were also strong enough to hold together when that long, the whole reason for 2 wings evaporated. Which reduced drag which increased speed which improved unit lift per wing area, which … in a very virtuous feedback loop.
The need for 2 wings was the logjam that prevented that virtuous feedback. Once it was broken the need quickly evaporated.
In general longer wings are better for cruising. cf. sailplanes and long-haul airliners. While stubby wings are good for maneuverability, both to enhance roll rate and the G-load they can sustain before failure. cf. F-16s, F-18, and earlier fighters as well.
Applied to interwar fighter tech, things like the e.g. Brewster Buffalo could already roll faster than the pilot could smoothly control. Unboosted controls were more of a limiting factor than wing length. And those aircraft could pull more Gs than the engine could sustain energy through over combat-meaningful time intervals or that the G-suitless pilot could maintain consciousness through.
Said another way, adding a second wing would fix a problem they didn’t really have.
If I were trying to design a 1936 ultimate fighter biplane I’d be aiming at two very short stubby wings, boosted flight controls & G-suits. That’d create maneuverability that would eat a Zero’s lunch. If you could stuff a big enough engine into it.
Today there are efforts afoot to build quasi-biplanes as airliners and as pilotless urban air mobility vehicles.
In the former case it’s about making much much longer sail-plane like wings for cruise efficiency that can’t support themselves without external struts. The difference today is we have the aerodynamic design chops to make the strut also a lifting wing, not pure drag as they would have been in 1935. This is one example of several such research projects: Boeing Truss-Braced Wing - Wikipedia
For the urban mobility mission it’s about making the vehicle footprint smaller so the landing & parking areas can be smaller.
Once you can do the CFD work, there are also aerodynamic and structural advantages to two wings that are connected to each other at the tips. Here’s one configuration but there are many others being messed with now days. A Physics-Based Approach to Urban Air Mobility | Drone Below
Some attempts in these directions were made in the 1930s. But the materials science, structural science, and aerodynamic science just weren’t there yet.
I have a minor quibble about your premise. you overstate a bunch how quickly radial engines went out of fashion. Your other design points are well-founded, but radials were still being specified in new fighter designs as late as the middle of WWII. e.g. https://en.wikipedia.org/wiki/Grumman_F8F_Bearcat was a vague notion in 1942, serious design was late 1943, and production stated in 1944.
Had jet engines been 10 years farther into the future than they really turned out to be, I doubt the Bearcat would have been the very last piston fighter and may not even have been the last radial-engined fighter.
To be sure, 1944 is only a few years after your target date of 1936. But it internet years’-worth of aero-progress was made in that short time.