Pressurising a carburettor via a supercharger brings with it a substantial number of problems. For a start, all carburettors operate on vacuum and venturi principles.
When you pressurise a carburettor, it reverses all the basic carburettor principles. Supercharger pressure means all shafts must be sealed to prevent fuel leaks.
The standard venturi effect does not compensate for air pressure. As boost rises, the carburettor can lean out, leading to dangerous combustion chamber temperatures, even broken internal engine components (pistons/rings).
It is difficult to keep a supercharged carburettor from running too rich at idle and light throttle, because the idle circuits are pressurised.
Carburettor gaskets must be seriously modified or eliminated, as standard carburettor gaskets can blow out, or leak fuel under pressure.
The boost pressure from the supercharger can force fuel past the carburettors needle and seat, causing the float bowl/s to overfill, flooding the engine.
Standard fuel pumps cannot handle a supercharged carburettor setup. You must use a boost-referenced fuel pressure regulator that increases fuel pressure in direct proportion to boost pressure. If the fuel pressure does not remain higher than the boost pressure, fuel will be forced backward, emptying the float bowl/s.
If the carburettor floats are not designed for high pressure, standard floats can collapse under the intense pressure of the supercharger, leading to a catastrophic loss of fuel control.
Supercharging a carburettor can lead to intake icing. As the supercharger compresses the air, the cooling effect of fuel vaporisation can cause intake temperatures to drop below freezing inside the carburettor, leading to ice formation on the throttle plates, even in warm weather.
The high-velocity air forced into the carburettor may not supply all air or emulsion bleeds in the carburettor evenly, causing some cylinders to run leaner than others.
In summary, the addition of supercharging to an aircraft engine via carburettor pressurisation, brings with it a substantially increased level of complexity in components and tuning requirements, which is not desirable in an application where that level of complexity lays the groundwork for increased engine unreliability.