The Mute button only affects voice chat functionality (as you already know), and that is by design. We don't have a way to selectively mute all sounds for specific users.
Despite what you said above, if someone is flying in a way that you find annoying, that is a situation where we would expect you to make use of the Hide button. It's not a permanent action; you can unhide them after a while and see if anything has changed.
Have you played with the multiplayer simulation sounds reduction feature? By default, simulation sounds (meaning everything in the Audio->Simulation Sounds category in the Settings dialog) are reduced to 15% of their normal volume within a multiplayer session. You can tweak that percentage in the Settings dialog by selecting Multiplayer->Simulation Sounds Reduction (%). If it's still bothering you at 15% volume, though, you might prefer to have simulation sounds simply turned off while in MP. You can change them from Reduced to Off by selecting Multiplayer->Simulation Sounds from the main menu.
I know it's not what you're asking for, but I hope it helps.