what is considered too much in resolution in frequency tuning and transmitting?
Nothing. You physically can't get arbitrary exact frequency within finite time (Heisenberg won't let you), but that's far from where you are.
On the contrary: since oscillators aren't perfect and have frequency error, you'd always want to be able to tune. There's no downside to that.
The question what's practical when someone turns a knob is a different one: If I was to build a radio, there'd be numeric buttons to key in the frequency I want. I'd simply stop typing digits when I think I'd be right.
Normal radios go in steps of .5 before going to the next band:
.5 of what unit?
Anyway, I don't think that claim is true. Radios have very different ways of selecting frequencies. For some applications, a 75 kHz channel raster is right. For others some other.
Capacitor types allow you get more inbetween which offers a better resolution
That's simply not true. Fractional frequency synthesizers have a very high resolution, and the remaining offset is trivially compensatable with numerically controlled oscillators of various architectures.
An electrically tunable capacitor only has as many settings as the DAC controlling it has possible output values. It's still a relatively inaccurate way of generating frequencies, so although you might think you have a high resolution, you actually just got many steps of relatively random frequencies.
A mechanically tunable capacitor is typically hard to actually tune very reproducibly and exact.
For these technical reasons, modern radio devices don't use undisciplined capacitor-based synthesizers at all – instead, they use the aforementioned fractional frequency synths (which can, in some instances, include an electronically tunable capacitor, but not necessarily).
So, wrong claim: If you actually want good resolution, then you need good accuracy, otherwise your resolution is largely meaningless. You get excellent accuracy with things that are not tunable capacitors.