That’s what players usually want.
I want it really low, but no buzzing. As low as possible without buzzing.
The thing is, it’s not just me (the setup and fret work) that determines whether fret buzz happens. Sure, I can adjust things nicely and fix any uneven frets but that’s only a (small) part of the picture.
There's another vital part to consider…
To do so, it might be helpful to think of string action as a ‘limiter’.
Action as Limiter
If you’re running a signal through a limiter, the hottest peaks can be clipped off or squashed down. If you want, you can adjust the limiter's threshold so that this clipping happens lower down, on signals that aren't as loud.
String action is a limiter. It restricts the dynamic range of your picking. It can move the threshold at which fret buzz kicks in. The 'hotter' (harder-picked) notes can buzz.
With a high action, strings are far from the frets and you can really dig in with your picking hand and get those big chords chugging along. Loud and clean. No fret buzz, no limiter. Yay.
As you lower the action, you also bring in your fret-buzz limiter. Now, hitting the strings hard means we get some fret buzz creeping in. There's less headroom for heavier playing.
The lower the action, the lower the threshold before fret buzz occurs.
The lower the action, the lighter you have to play to avoid buzz.
And, while there are setup steps and fretwork that can improve things, the ultimate limiter on whether you’ll have fret buzz is you.
And physics. It's always physics' fault.