As far as the alternate greens go, here's a little bit more info.
#6--This one gets the most use of all of the alternates...although this has become the case a lot less over the last few years. There used to be a lot more tree coverage over the usual 6th green's right side. The Club, for a long time, had grow lights that hung over the 6th green to provide an artificial replacement for the lack of sun that green would get. It is for this reason that it is a well-known fact among the membership that the sixth green is the slowest on the golf course. For the same reason, it gets the most rest and thus its alternate gets the most play.
#10--This alternate green usually only got put into the rotation on Mondays--the day the Club hosts charity outings. Rarely would the Club ever put this into use Tuesday-Sunday. I'd imagine the reason for having this alternate is the super-small regular 10th green...in conjunction with the fact that this green rarely receives anything more than a wedge shot and thus takes more of a beating on pitch marks than any other.
#14--This is the most recently built alternate green, but its status as an "alternate" is something of a misnomer. It was built a few years ago when the regular green was rebuilt (to bring it in closer to the front bunkers). The reason why they built this was so the members would have an actual green to play to while they were doing the rebuild. Since the regular green re-opened, I've probably seen this green used less than five times. None of those times were Tuesday-Sunday.
#16--I assume the rationale behind the alternate green for this one-shotter is derived from the same rationale as the alternate green for #10. I'm not sure which of the two greens has the lowest square footage but they are both easily the two smallest on the golf course. Given the hole's modest length, it suffers from similar pitch-mark issues as the 10th...maybe even more so because it's a wider and somewhat more accessible target. For a hoot, play this alternate green from the old tiny back tee on 16. At 140 or so yards, its no bargain.
One thing worth pointing out, to address your point about being a guest and having it suck to only play 14/18 real "Riviera" holes, is the fact that almost never has the Club put all four in play in a single day. If the 6th is an alternate, the 16th will be the real green or vice versa. Usually, if there are any alternates in play, it will never be more than one or rarely two. If it's two or more, I'd be willing to bet my natural life that it's a Monday.