Sorry, I don't see it that way.
If you sample your ~800 MHz signal at 1600 MHz, you'll have a bunch of discrete sample values, each one about 180 degrees farther along in your signal's ongoing cycles. Since the stepping is not exactly 180 degrees, your samples will wander up and down - sometimes they'll be near zero (i.e. when you're sampling at zero and 180 degrees through the signal's sine waves) and sometimes they'll be higher, say +/-58, because they were sampled at/near the high and low points (90 and 270 degrees) in each sine wave. So +/-58 is the maximum output created from the sine wave's voltage feeding into the ADC.
So - at any given point, let's grab a sample - here's one and it's a 7; so what's the signal's strength at that point in time? We'd like to AM demodulate it, so we need to know the signal's RF strength at all points (or maybe every nth point, since we probably don't need that much time resolution). How are we supposed to get that from a 7? Or more importantly, how much work (math or data transformations or whatever) are we going to have to do?
Let's say this ~800 MHz signal is actually a dead carrier (constant RF power), but with non-I/Q sampling, we're handed a bunch of numbers that wander from zero to +/-58 - how do we take a sample at time x and say "RSSI=y"? We can't do that with a single number, or even with that number and its immediate neighbours, can we? Even if we can, can it be done with simple/fast math?
Meanwhile, with I/Q data, every time we sample that sine wave, I and Q get set to sine and cosine values that tell us where in the sine wave we are (e.g. what angle we're at) and the sine wave's magnitude/power at that instant in time.
RF power is just the length of the line from (0,0) to (I,Q), and since I and Q are 90 degrees apart, this is a simple Pythagoras problem (a squared plus b squared equals c squared, according to Google), so we take (I times I) plus (Q times Q) and voila, we have a power level at time x; do that at regular intervals, say 24,000 times a second, and we have AM demodulation and audio that can be sent to a speaker.
Examples:
If we happen to sample the signal right at zero, 90, 180 or 270 degrees into its sine wave, we get an I/Q pair where one of the values will be high (plus or minus 58 with our dead carrier), and the other will be zero (because it's 90 degrees off), so when we need to calculate power, we get 58x58+0x0=3364; same for -58x-58+0x0, etc.
If we sample 45, 135, 225 or 315 degrees into the RF signal's sine wave, I and Q will get set to the sine and cosine values of those angles, which are all plus or minus 0.70710678118, multiplied by the signal's magnitude, which is still 58, so we get +/-41.01219330844; when we want to know the power level, we wake up Pythagoras and get (41.01... times 41.01...) plus (41.01... times 41.01...) is... 3364, same as above. Same as above for any angle into the RF signal's sine wave.
If the signal's power level is not constant, our (IxI)+(QxQ) calculations will give us numbers that vary in direct relation to the RF signal's changing power levels.
For FM demod, we treat an I/Q pair as a dot on a circle. And the next I/Q pair as another dot. The angular distance between those two dots on the circle is a signed (positive or negative) angle measured in degrees and is easy to calculate (simple atan2 function). That angle tells us the instantaneous frequency of the RF signal. It also tells us what audio value to generate - a small positive angle change = a small positive audio sample, let's say +125; a big positive change = big audio value, let's go with +27,445 (that's fairly big for signed 16 bit audio); same deal with negative angular changes - we get negative audio values. Send those audio samples to a PC's sound hardware and we hear the FM signal in all its glory.
Now how do we easily/quickly generate FM demodulated audio from the non-I/Q stream of samples? Since we're sampling at almost 180 degree intervals, that 7 from above will likely be followed by another 7; a -58 by another -58; a zero by a zero, etc. So how do we get instantaneous RF frequency?
So:
I/Q data --> AM or FM demod = easy peasy, aka not "a hack"
A single stream of RF values --> AM or FM demod = how to do it? (it has to be simple and fast or it's pointless, since we already have a working easy/simple/fast approach)
Edited to add:
This doesn't even get into all the other useful things that I/Q data enables, such as the ability to losslessly rotate the entire spectrum of signals that an SDR has grabbed, i.e. to shift any targeted signal to baseband or wherever else you want it without the need to filter out or otherwise worry about the other signals that may be present in the SDR's passband. Again, how do we easily do that with non-I/Q data? Mix that data with a "shifting" signal? Now we've got aliasing products all over the place, including over our target signal...
And so on...
