Well most people who sign up don't have an appetite for "online correspondence" chess. They rush straight to the live chess part and jump into blitz or other forms of live games.
My experience as a greeter.

Well most people who sign up don't have an appetite for "online correspondence" chess. They rush straight to the live chess part and jump into blitz or other forms of live games.
Understandable, but starting the greeter game is optional. Is EVERYONE so stupid that they start something they don't want to participate in? I could see half, but everyone?

Most people don't know about the optional part. I didn't the first time I signed up!
Plus I've had a few think that this is a live game they are playing ... I get a chuckle when log in the next day to see the adorably cute "Why aren't you moving, you slow @#$@#" message.

My own greeter experiences are very similar to your own baronspam, except I have yet to get to move seventeen(!). How can they join a site, have a guide laid on and then have zero questions? I wonder if the process that they sign up to is properly explained because I've had odd replies when I offer to answer questions e.g. "why?"

My experience was similar. Could it be that they're like me (and possibly even you, Dear Reader), in the sense that they came to chess.com expecting to win a bunch of games?
Mmmm, good! I'll have another helping of come-uppins!!

How long did it take for you people to get your first greeter match going after singing up to be a greeter? I thought that I would get to play against those new joiners almost immediately, but haven't gotten a match in three days. Maybe I am too impatient?

Just guessing here: Chess.com claims to have some nationality/language matching (I forget which, exactly) with the greeter games. Perhaps, showing a small country flag (population-wise) and having a very particular language shortens your chances of being allocated a game.
As I said, just guessing.

i don't think it's likely to be nationality/language based. my flag reflects residence not nationality - i'm a native english speaker, but the system won't recognise that.
i am matched against various nationalities in welcome games and have played hundreds of them. i would estimate that 90%+ of my opponents have said little more than 'hello', so it wouldn't matter anyway. and the most common response to offering help has been 'ok'.
the majority of mine have timed out too, but there are a few that go the distance.
saksipotku, i expect the reason that you are waiting a while is your average move time. standing at over a day, that is quite slow in relation to the expectations of new members that want a fast game. my average move time is 6 hrs, and i receive new welcome games almost as soon as the old games end.

I've asked elsewhere if there's a maximum average time per move chess.com will accept for greeters, and I haven't found or been told an answer. I've just seen some speculation by non-staff. You'd think if there is a cut-off it would be published somewhere (like how about right next to the greeter game setting?) so people don't volunteer/sign up to be greeters and then wait around to be assigned greeter games that will never come their way, which would be a shabby way of treating people trying to volunteer some time to the chess.com community.
Having been on this site for several months and having enjoyed it, I thought that I would sign up to be a greeter, one of the people who plays a unrated "welcome" came with new members. Of the six games that I played, I won every one on time. The longest was 17 moves, the shortest was 1 move. I welcomed each new player and asked if they had any questions. Only one replied, and he just said hello. Maybe six games is too small a sample to really say, but based on my experience, I am no longer a greeter.