That's the fun of floating point. It actually really shifts the decimal point to preserve given number as precisely aspossible.

I think what happens in daw when you gain something is, that it tries to multiply the samle value by gain amount. It probably takes those numbers, loads them into SSE vector and sends it to CPU for computing. Modern CPUs have so called FPU coprocessors, which are blocks dedicated just to dealing with floating point operations. Those probably find out how much decimal point shifting is needed and try to preserve the precision while doing so. That's why you didn't end up with quantized stair hills, but neat sinewave at the end. It just shifted decimal point, leaving the "values" themselves almost intact.

I got ya. But also I don't think any precision is lost while gaining the same signal. It just shifts the decimal point and does some small multiplication to move the values inside of the target range. Better test might be this: Make full scale 0db sinewave, mix it with -100db one, render it out and check how the quiet sinewave survived.

This is partially why I think it's still not a horrible idea to leave headroom.

science aside, i think head room is nice because it definitely gives your tracks room to actually breath an entire breath if it needs to. the varying level of the breaths it takes also gives you different feelings as it hits into your effect chains.