Educate me about gain and amp/preamp matching

Look at it this way: assume two cars with the same engine are accelerated to 50 mph. The first car requires the gas pedal depressed 1-inch and the second car requires the pedal depressed 1.5-inch. Both have a different gain but both have the same maximum hp and both are putting out the same power. The only differences are the second car may run out of pedal before max power is reached;  the first car will still have pedal travel after max power is reached but nothing changes in that extra travel.

I’m actually surprised that the input gain of a preamp doesn’t really effect the output signal gain of the amp. I thought it would be additive or multiplicative (if that’s a word). Can someone explain why that is?

Amplifiers are fixed. All an amplifier does is take whatever comes in and multiply it by some fixed amount. That fixed multiplier is the gain. 

But it can only do this to a certain point. In your case 30W. At that point it doesn't matter how much more you input, or how high you turn up the volume on the preamp, that amp is not capable of putting out any more power. 

An active preamp is really nothing more than a small amplifier with an attenuator (aka volume control) and some knobs to let you switch between sources. That small amplifier is fixed just like the power amplifier is fixed. Same deal. 

All your sources connected to the preamp, they all are at line level. Line level is a couple volts. (The exception is phono, which is in millivolts, which is why turntables need a phono stage, to bring millivolts up to line stage voltage levels.)  

Now here's the thing- all your line level components have more than enough power to drive your power amplifier to clipping, ie as loud as it will go. 

So in practical terms the gain of the preamp is irrelevant. More often than not its not amplifying anything, its attenuating. 

If you have something like a CD player with variable output you can prove this yourself by simply connecting it directly to your power amp. It will drive them just as loud just fine. It will probably not sound quite as good. Why? That gets a little more complicated to explain.

These are all incredible responses, thank you. I think I misinterpreted Cleeds’ answer  because you explained how I actually believed it - the amp always puts out the same amount of power, and the preamp’s power can add gain (if it is active). Together, they are additive, and the preamp’s volume control attenuates the whole.

i’m guessing the idea of headroom then is similar to a well-exposed photograph in that it has the most amount of dynamic range and is uncompressed. Having a preamp that has a lot of gain may also add noise, depending on quality, and sending that to the amp could amplify and raise the noise, making sound have a lower range. Per @millercarbon’s post, it might be that the noise balances between the amp and preamp are what can make a preamp truly successful, as the right match may result in the right blend of 2nd order harmonics, adding body and texture without losing overall range. 
The amp also has to be able feed the speakers with the power it needs to be able to handle generally what is hungry (usually the bass) and still have enough power left over to handle the rest of the frequency range, otherwise it will clip. 

I did this type of exercise last night with a different amp, just to test, which is why I decided to post this thread. The amp in question was a 2W/channel Korneff 45 clone. Of course, I knew pretty well it wouldn’t be able to drive the Quads, but I wanted to experiment even at very low levels. Oddly, combined with the Viva Linea preamp I would have been able to get the SPL I wanted, but the sound started to clip even before the volume was at 12 o’clock. I took it off right away.