I know we are a community and such. But I'm one of those people who likes to Know a person and actually be friends with them. Instead of having a bunch of friend requests coming in from people I don't know. So I'd really like to be able to turn them On and Off at will, so if indeed I want to become friends with someone, I can turn it on so they can request, then off once more after.

Perhaps, if someone really likes a person's pets and likes to watch for them to have anything they might want to buy, why not have a way to bookmark a person on the site itself. Either allowing the owner of the character to know how many people have bookmarked them, or not. But a way so people don't feel the need to friend request someone just so they can watch them.

I think this is a good idea.

I also think that being a multiplayer online game should facilitate community, but this feature would be appreciated as an option.

I sometimes get friend requests from random (probably new) users, but they have never talked to me in any instance (neither region chat, general chat, forum, nor PM). On my About Me (and several other users' About Me's), we say "we don't accept friend requests unless you've talked to us before", or something along those lines.

I reject their initial friend request and instead send them a PM asking if they're enjoying the game or if we've met. Sometimes they answer, sometimes they don't.
If they're a newbie wanting help, I'm all up for offering it if they need it aha.

Having the "Add Friend" button disappear on a profile is a good way to control communication. You can still message the person (via Send Message), but it removes likeliness to get unsolicited friend requests. It still gives us the option to add someone else (if their Add Friend button is on).

Maybe accompanying this, the Social page should have a way to send friend requests to others, to allow those who turn off their friend requests to send out those of their own.
(A suggestion for the revamp, because the Friend Requests now are two-fold, where I have to add someone and they have to add me)

I know this feature might help only a small niche of users, but it could be helpful in whatever reason people have to turn off their friend requests.