A satellite dish does not transmit any information to the satellite. Satellite TV is a pure broadcast system in the forward direction.

Moreover, comparing a parabolic receiver with a phased array is quite unfair. The amount and complexity of the electronics and processing power required is several orders of magnitude different.

A better comparison might be HughesNet. Not perfect since it's different classes of satellites, but their modem is spec'd at drawing up to 60 watts on their latest gen. Though, in practice, it tends to draw around 15-25 watts, at least according to comments I can find online.