Your logic is reasonable here and your conclusion is representative of many intraday methods based on MAs. I have seen many where the shorter MA is 5-10 periods combined with a longer MA of 10-20 periods (e.g. the HLHB system on this site).
The choice of MA type is also mainly EMA rather than SMA on these short term methods for the same reason - they react quicker.
BUT… the same benefit (i.e. quick reaction time) that make these attractive is also the reason for their frequent downfall - whipsawing in tight ranging, or drifting, markets.
And we do not know until after the event whether each MA signal is the start of something big or just another short term flip. Afterall, when comparing a short term MA with a longer term MA one is always on one side of the other!
This is why, although MAs can be good indicators for entries, they usually need some additional technique to provide confluence in an attempt to avoid fakeys. E.g. the use RSI and ADX in that HLHB method (just as an example).