Input impedance has nothing to do with gain.
You can have a high input impedance on a solid state amp by using FET devices at the input.
Large solid state amps with a low input impedance often do have a lot of gain as they are designed for use with loudspeakers that need a lot of power. You need gain for that- 30 db might barely be enough. Conversely if you are driving a horn speaker you don't need nearly so much gain so many SETs don't have all that much- sometimes 15 db is plenty.
So there is a rough correlation but it is not based on input impedance => gain.
You can have a high input impedance on a solid state amp by using FET devices at the input.
Large solid state amps with a low input impedance often do have a lot of gain as they are designed for use with loudspeakers that need a lot of power. You need gain for that- 30 db might barely be enough. Conversely if you are driving a horn speaker you don't need nearly so much gain so many SETs don't have all that much- sometimes 15 db is plenty.
So there is a rough correlation but it is not based on input impedance => gain.