Why Rhodium?

Yeah, but the red, hot stamped Rhodium...
I'm waiting for the Cobalt.

I agree with Buconero. Rhodium plated connectors are, IMHO, a fad. Until recently Rhodium was cheaper than gold, and it does resist corrosion better than PURE silver plating. But it is not a preferred surface for wearing thrust contact conections. Mil-spec and industrial standards call specify gold as the preferred contact surface for gas tight cold contact electrical connections.

On top of that, you guys are kidding yourselves if you believe that the material used for the connector plating will have an enough effect on a signal to be audible, if even measurable.

ANY time 2 different metals come into contact you form what is called a junction. It is called a thermocouple and produces a (minute amount) electrical current. While I wouldn't expect it to be a factor in power or power supply, it could be a large fraction of low voltage circuits, like phono.
This effect, (thermoelectric effect) should drive those nuts who can hear which way a fuse is installed in a power supply.
Rhodium is used in such couples, for many of the properties listed above.

Don't believe me? Get out a steel coat hanger and a piece of #12 copper wire.
Twist the ends firmly together. Use a vice and pliers if you have to. Connect the free ends to a DVM (what? You don't have a DVM? Shame!) and stick a match under the junction. You should get a couple MV, at least.

On top of that, you guys are kidding yourselves if you believe that the material used for the connector plating will have an enough effect on a signal to be audible, if even measurable.

yes this is why, for example if you compare the Oyaide 037, 046, 079 plugs which have the same exact construction except the plating, being silver/rhodium, gold/palladium, and gold/gold respectively, and you put them on the exact same built cord they sound exactly the same! The different color ends are only for WAF and for the fashion conscious audiophile so as they don't clash with the rest of their system.

IMO, the issue is more complex than just conductivity of the plating as a cause for differences in sound with various platings materials.

The FI-28M(R) appears to be the “little brother” to the FI-50, both being made of rhodium over pure copper. I suspect the sonics are similar. I've found the FI-28M(R) to have excellent dynamics, smoothness, transparency, detail, decay, and soundstaging, while remaining tonally balanced, with no glare.

My rhodium plated Kaplan cable sounds slightly more lively and detailed, as compared to the pure copper version. The cordage is the same.

I know that some rhodium connectors use a silver underplating. Perhaps that is the source of the glare?

I don't believe that rhodium will necessarily cause any loss of detail or transparency, as compared to a higher conductivity material. My experience is just the opposite.

I’ve also tried the FI-25Gs, but they sounded somewhat bright, with some glare.

Another example of interesting material is palladium. I use a Pure Note Alluvion digital cable, and the palladium in it sure takes the glary edge off of the silver. However, this is an alloy, and not a plating.

Nickel is another story. It always seems to cause glare for me.