Linkedin should be seen as a channel to be connected to people and expand network. it is channel among other which allow this but it s has a professional value and self-promotion tool.
I think that the best way is to be multichannels and trying to connect to people in all the space where they have account . and the best is that other channels let you to be connected to people in linkedin at the end
for example, the first time that I was connected to you is through twitter, you have make the connection easy by promoting your blog which contains link to ziki, linkedin facebook etc so I was able to sent you request in all these spaces.
you can having connections in only one space ,other in some spaces and people in all spaces.
that raises for you opportunity to self-brand, self-promotion and participation ( and we shouldn’t forget your blogs).
the value isn’t in number of connection (no need to be connection’s hunter) but in the quality of interaction and knowledge share. if I add connection I have to interact with him/her and share interests.

PS I have sent request to customer service and they replied to me 🙂