I work with a company that sends iMessages from their iOS application. We noticed recently that our messages with links are not clickable and do not show either the web sites favicon or previews.
After doing some testing, we have determined that the problem is as follows: (I would love to have someone from apple confirm these findings)
When someone sends a message to a user using iMessage. If the receiver is on iOS 10.2 and does not have the sender in their address book, the links are not clickable. The work around, which is not a good one, is to have the receiver add sender to their address book. Once completed, even older received messages become clickable.