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View submission: Why does weather radar only use one spinning dish?
Short answer: Cost
Long answer:
You're partially correct, you could triple the dishes and get the sampling rate up, but to what end? The current rate is fast enough for meteorological purposes. More detail or faster results won't necessarily improve weather reporting.
However, even if you did put three dishes 120deg out of phase, you would not increase the resolution, just the sampling rate. Resolution is governed by the size of the dish or really the effective capture area of the return signal (see synthetic aperture radar, SAR). If you put three dishes right next to each other, you could sync them to act like SAR.
But why wouldn't you do this? Cost. It would be more than 3 times the expense without 3 times the value. Unless you have a specific application where you really need that resolution or sampling rate (which do exists and very expensive, advanced radar systems have been made for these needs).
There's nothing here!