I tried this also, and I don't think by adding favorite and naming the mailbox, that what you are seeing is the inbox. Infact it seems to just be basically searching for emails to/from that address. I can see by the "in folder" tags that the emails displayed are from any number of folders (sent, deleted etc). So it seems to be more of a search than to promote a folder to favorites like you could do before.
I have 5 shared mailboxes which I need to monitor. My personal mailbox is the least interesting, frankly I work out of the others. Even the Inbox on those shared mailboxes are not of interest to me. Under each mailbox I have certain folders allocated to me, those are the ones I need to watch, so promoting them to favorites is the perfect solution. Now I have to basically extend all the mailboxes, folders and subfolders to monitor the ones I need. It's totally inefficient.