Doesn't matter what the icon is people will chase it "just because". Either because they're achievement hunters or consider it a status symbol. One change that would partially mitigate this would be to only make it visible in NN chat or if the mentor queued via Mentor Roulette.

Whispers are less than ideal. Not everybody knows everything. A shared channel has a much better chance of connecting with somebody that can help instead of iterating through all online mentors and hoping they can help. If you funnel everybody into 1:1 conversations that can quickly lead to mentors getting overloaded (eg. the last name starts with 'A' problem) and not everybody is all that comfortable cold calling people.

The other big drawback to whispers is that excludes people on the free trial. Before you sneer those are exactly the kind of folks that the mentor program was set up to handle. New players that aren't sure enough that this game is for them.