Why Rhodium?

It's shiny, but most of the time I find it too hard and slick to offer good grips.

I like my contact metals soft and springy. Hard spades for instance are nearly impossible to tighten well long term. Gold over copper however has enough malleability that the speaker terminals bite into them when tightened.

In power connectors they seem to make it a lot easier for plugs to slide in or out.

I love how they look.  Like jewelry, but never had a good experience with them on a practical sense.

I use Oyaide C-004 on IEC and Viborg Silver/Rhodium on Schuko in my system. My observations is that the plugs not only have an effect on the frequency repons (less warm, more neutral) but also on the time domain. The hard metals don't have the "soft" 'decay' of gold and silver and present a tighter sound with more 'attack', punch and control. They suit my taste of music (rock/pop), but I understand that not everyone likes them.

1. Poor conductor
2. Hard which makes for reduced mating contact surface.
3. Only used in audio
4. Uneducated consumer

I am sure there are more reasons.

Current estimates are a leading edge semiconductor plant costs $10-20 Billion (that's 9 zeros). Even a large geometry analog fab is high 100's of millions. I.e. price is really no object. You will not find one rhodium plated connector in that plant.

It’s interesting that folks who actually have a credible story / testing to tell about their experience with rhodium connectors vs gold, etc all agree that rhodium is a superior connector metal / material with least impact to the energy and openness of the music signal. 
 

those who don’t have any experience to speak off think it’s a bad connector material. And will never try it. 

Rhodium is not only a poor conductor but IMHO too hard.

To get a good grip on an outlet or speaker or any other contact you want a soft metal.  Something that will deform under pressure, allowing for serious grip, especially for AC plugs, sockets and spade connections on speakers.  Pure copper or gold plated copper will absolutely outperform Rhodium for reliability alone here.

Rhodium, as pretty as it is, is really a terrible choice in this manner.