My gut feeling is the signal dimensionality of each of the I/Q is less than that of the composite.

M.G.Rajan

Hi,
My two cents on this thread:
1) You can perform the I/Q demodulation directly in the digital domain(it's not needed to provide the DSP with and I/Q path, the transformation it's just a multiplication with a sin() and a cos() easily done with C or whetever use the digital processor).
2)If you have a quadrature modulation and want to the demodulation directly in analog domain(less power consumption) you must provide the I/Q path to implement the analog matched filter( a simple correlator), I've seen this in extremely low power applications.
3)Although that it can seem a bit strange it can be useful to provide a I/Q path in the analog domain while your signal it's something like a FSK, if you don't recover the phase of the incoming RF signal your LO can be orthogonal sometimes to the carrier thus losing all the energy(due to effects of the channel,like a Rayleigh distribution common in f<10GHz or so), if you use a couple of Mixers with LO in quadrature you will have in your worst case energy in the Q path and usually you will have energy at both branches(I've seen this in zero-IF receivers and I think it's usual also in low-IF receivers).
Hope it helps,