The procedure written above is as is written in AFM, so it's what the manufacturer thinks is best for the aircraft. This is not flooding the engine, it's priming - just that in the old 1930's engines (C172 & similar spam cans) you have carburated engine, which has a manual primer, while the "new" injected engines just use fuel pump and fuel injectors to prime the engine (and it's much better because you prime all the cylinders, not just one like in O-320 for example).
If the engine appears flooded, maybe you could try switching the fuel prime (high speed fuel pump) OFF before starting the engine. From my memory some engines start better sometimes with the fuel prime off, but if you do use fuel prime pump during cranking, ensure that throttle is open just a bit, because with fuel injected engines, fuel flow is defined by throttle position (that's why the AFM says to use full throttle when priming - to achieve maximum fuel flow and thus decrease the time of priming) - and setting throttle a bit more open for the start will only lower the chance of successful start in most injected engines.