Why 300Bs?

Simplicity, purity, linear, euphonic and most importantly: class-A operation. Depends on how much power you need, it is probably the same reason why folks go after other SET output tube amps like KT88(in triode mode), 845, 211, px25, 2A3, and 45.
The cheaper version would be EL84 SET which also sound quite good too. In most cases, the bigger the tube the more power and more stability you get.
You need to get out more often to hear one. Start with the famous Jadis 300B amps then listen to these Chinese clones. In my opinion, you'll notice that all 300B amps are not create equal.

Call Kevin Hayes of VAC -- he'll tell you everything you ever wanted to know about 300B output tubes.

I think it's really just SETs in general. They must be heard to understand. Either you'll love their natural sound or you'll come away thinking "I don't get it." As for me, the jury's still out on SETs. But I probably haven't heard my magical combination yet. I loved the DIYHiFi 300B amps with Omega speakers. And the Cain&Cain Abbys with Audio Note 300B were nice too.

The 300B amps (or lower powered SET amps in general) are often paired with higher efficiency and high sensitivity loudspeakers. The most common are simplier single driver (no crossover) speakers and single or multi-driver horns. Some feel the SET topology coupled with high sensitivity speakers allows for the ebb and flow of music with its subtle nuances to be felt. So far the best example I've heard is Tpsonic's 845 SET with modified 9ohm Gallos. But that's a different animal than a 300B.

No I don't understand why the 300B in particular commands the price it does compared to other tubes or even other SETs. It might have something to do with the Japanese audiophiles who some credit with restarting the SET resurgence. It might be the modest power (compared with flea power 2a3 and 45 tubes) and the fact that higher power 572 and 845 tubes don't have the famous history that the 300B does. Many others have a different view. I just see the 300B as a another lowered powered tube. But then again I don't have much experience with that tube, or a lot of tubes, or even audio in general. So weigh all of that when you read my opinion.

Aaron