We don't know how rare either actually is. For both we have just one example - us. This suggests odds of no more than one in several thousand. But it doesn't

We don't know how rare either actually is. For both we have just one example - us. This suggests odds of no more than one in several thousand. But it doesn't take too many filters of that order of magnitude for a few hundred billion to become a handful, and the handful to become just one. Your point about binary star systems is interesting. Orbital dynamics have a well-known tendency to be chaotic. In a single star system, this chaos is significantly less of a problem. But in a double star systems, the odds of moving in/out of the habitable zone over time are much higher. So that's probably a filter. But not as big of one as the ones I listed.