Two of my local leagues have gone to the poker chips with numbers written on them. The numbers are from 1 to 150 and one "pick your own partner chip". If there is an odd number of players then there is a "voluntary" flip off for Cali ( one player plays alone but gets one soft mulligan per hole).
It is sort of a shame that the Cali option exists because if one of the top players gets Cali it is almost an unfair advantage. Of course, if a very weak player were forced into being Cali it would be a huge disadvantage. I'm not sure there is a better alternative, though. It seems a little harsh to exclude the last odd numbered player to register.
I am also not fond of the pick your partner chip. I guess it is just as random as drawing any particular partner but something about it seems wrong.
A Pro/Am split creates generally fairer teams. The best thing about a random approach (where the best players might get paired together) is that the good players like it. If the good players aren't happy with a league format then they just go off on their own and play. For young or developing players there is a big benefit to playing along with and observing good players. They might "pay" for the privilege but no one becomes good without paying some dues.