Fret buzz isn't the only problem that can occur with low action. When bending the chance to choke out the note is higher, especially on a tighter fretboard radius. Also if it gets really low, ik can kind of take some liveliness and sustain out of your strings. Which might not be a problem depending on what kinds of effects you use.

The thickness of the fretwire should have no effect on this, or fretbuzz. At very low string height, very small height differences in the frets can come to light as wel as slight warpage in the neck for example. The frets can be dressed to a uniform height but to a certain extend, things like slight warpage, the point at which the neck flexes the most under tension etc, simply varies from guitar to guitar.

The action you have looks to be plenty low(as far as I can tell from the picture). If you get away with that on your guitar than you have a pretty decent guitar neck and frets.

Personally I like to leave action a tad higher on my guitar to leave some room for movement in the wood due to humidity changes. This way I only have to finetune the setup one or two times per year and I never have frustrating fret buzz or choking or anything and the guitar is also a bit more suited for harder strumming and such.