Resizing a 18MP image to 10 MP using a decent algorithm is not very much different to using a 10MP sensor with larger pixels in terms of signal processing.
In theory you are right but in practice you are wrong.
What you are saying is true only if the two sensors collect the same amount of light.
Consider this, though - the top surface of a sensor has an 'active' area (which collects light) and a wiring area (basically a dead area in terms of light collection).
More pixels on a sensor requires more wires.
If two sensors use the same wire size, more wires = larger dead area (and hence smaller active area).
So, an 18mp sensor will actually collect *less* light than a 10mp sensor - if both sensors use the same size wires and everythng else is the same.
FYI, Canon has not shrunk the wire size of their sensors since they started making sensors in 2003 (?).