Edit: Have I missed the point? I'm sure LinkedIn is a little more cautious about such changes than your average newly-founded startup. This product gives them access to people emails which they can probably glean a lot of info from. They already try to get access into email accounts (username + password) via the LinkedIn webapp so in a way this is just extending that to mobile. The only reason I can imagine them shutting it down is if no-one uses it (in which case, no one will complain).
You mean besides job agents, Answers, Events, ...
Perhaps my claim is weak and my knowledge limited but I find it more ridiculous to claim the inevitability of a closure before a product is even being used.
NB I feel I should add that I'm not going to be a user of this product as I won't hand over email access. However, I can imagine many people who don't think the same finding it very useful.
(If yes, you should probably ditch reading email and do something more productive with your time, like picking up cans.)