There are only 3 things about amp and speaker compatibility:Lets focus on those cases where the amps are not 'compatible' with those speakers?
How or why? I mean if we look at the amp measurements, any differences are usually below our hearing.
So using your logic... if the differences are in audible, what makes the pairing not compatible?
1. Does the amp have enough power for the speakers in the room to play at the required level without clipping. Power before clipping is measured.
2. Does the amps output impedance interact with the speakers impedance curve to change FR. This is only a concern with high output impedance amps like some tube amps and it is measured.
3. Does the speaker present a load that is "too low impedance" for the amp to handle. This is harder and not always measured buy Amir does measure this.
If you know the measurements of your speakers and your amp you can figure out if they are compatible and even how the FR will change in the rare times this comes into play. No mysteries or magic involved.