I'm aware than many carburetors are installed on manifolds over Bakelite or alike heat insulation plates, to reduce heat transfer from manifold to the carburetor. Some other designs use just a sheet metal plate, perhaps with a dubious efficacy. After a little research I see almost all the install designs uses some sort of heat insulator. However, how transferred heat would affect a carburetor's performance? I guess fuel vaporization happening by heat and other factors would help to create a better fuel/air mix? So, excluding the possibility of having the carburetor mechanisms and soft metal parts being cooked by the heat, is there any other reason concerning fuel, or the mix? Premature or out-of-the-place vaporization? Vapor bubble locks?
Other answers are sort of in the right wheelhouse, but I think you answered your own question with "Premature or out-of-the-place vaporization" ...
Any atomization is good, with the exception of before the "metering" element, whether that's an emulsion tube, venturi, jet, or injector resorvoir or thimble.
The problem is that quasi-vaporized fuel is difficult to measure and control.
Would you accept a glass full of beer foam (aka "head" [not my term]) at half price? Can you predict how much actual beer might settle out?
In terms of an injector, aerosolized fuel is problematic to inject, as the air bubbles are compressable, and most injectors simply work off of a pressure x injection time strategy... with the implicit assumption the fuel is largely a liquid -- not a pre-vaporized unpredicatable animal.
For a carb, jets have somewhat the same effect (and affect), and emulsion tubes (sorry, I'm old, skip a bit if Weber doesn't mean anything to you utes) expect to emulsify a liquid, not further emulsify a foam.
So, yes. While small droplets and complete atomization and lots of swirl and uniform A/F ratio is paramount, most engines are designed to create the fuel charge at a certain stage with known "liquid" and "air" sources. No skipping ahead.
One exception is GDI (Gasoline Direct Injection), where a realatively lean and possibly un-ignitable fuel-air mixture is augmented by a small thimble pocket A/F charge in a small depression in the top of each piston. This provides a "fuse" or "blasting cap" for the rest of the comparibly lean mixture in the cylinder. Still, all fuel is liquid and all gasses are gas until the magic moment.
I guess fuel vaporization happening by heat and other factors would help to create a better fuel/air mix?
But the mix is a precision control affair, and was set with reference to some expected range of parameters such as air and fuel temperature (and pressure).. Not sure that I agree that adding heat to the process improves the fuel either; atomisation is a physical process rather than a chemical reaction and because a carb is a set-and-forget device there isn't really scope for altering the amount of hotter gasoline added to the less-dense, hotter airstream
All these things said, I think the heat shielding of a carburettor is probably more important in the sense of "hot engine is stopped and parked up" sense in a similar way to "don't park a car with a hot catalytic converter over a patch of dry grass"