I don't get why you wouldn't join... (Keep in mind that everything I'm saying applies only to the US.) You simply can't collect performance royalties and broadcast music royalties without joining ASCAP or BMI. It's not like Harry Fox, where you can join and have them collect your mechanical license fees, or you can do it yourself (which is what I do), since the law requires that a piece be licensed to be recorded.
To play devil's advocate, I'll point out that ASCAP and BMI don't license churches, so if you have choral music that's only performed in churches, the performance licensing doesn't apply. But let's say Chanticleer records your choral piece. Their record label will obtain a mechanical license from you, regardless of whether or not you belong to Harry Fox, so at least that license will be covered. If that recording is then broadcast on the local classical radio station, unless you belong to ASCAP or BMI, you won't get a broadcast royalty. Radio stations pay those license fees to ASCAP and BMI, not to individuals.
What if Chanticleer performs on a Christmas special on NBC, and they perform your piece? Again, if you don't belong to ASCAP or BMI, you won't get the broadcast license fee, because again, the broadcast networks and cable don't pay these fees to individuals. Fees are paid to ASCAP/BMI, cue sheets are provided by the network, and ASCAP/BMI distributes the royalties.
There are venues not licensed by ASCAP/BMI (churches, high schools, middle schools, athletic events, military bands, and on and on), and I guess you can argue that if 100% of your music will only ever see those venues, you don't "need" a performance rights organization. But don't forget about things like the ASCAP "PLUS" awards, which are annual grants given to composers whose music is performed primarily in these unlicensed or underlicensed venues. I know one choral composer in the US who doesn't get much regular ASCAP money, but he does get a $5000 grant from them every year in recognition of what he's doing outside of normally licensed venues.