Stage 1. Organizations would use it to create _internal_ messaging systems, for employees/members only. At that stage it does not replace e-mail, and both systems are used alongside it. If it is mandated to be used for internal communication, this solves the problem of getting "Open this immediately!!!" e-mail claiming to come from your boss, but being in fact from scammers. It also solves the problem of e-mail from your colleagues getting into spam folder.
Stage 2. If your clients, suppliers, etc. start to use mnm, you can add them to your mnm network, and stop using e-mail in communication with them. When you reach this stage, you can severely reduce using of e-mail for your organization, at this point perhaps the only people who need e-mail are marketing, support, and perhaps developers (but the latter only for maillists).
3. mnm gets a critical mass, where it makes sense for organizations and projects start to offer mnm as an option to contact them, and later to require them. At this point "general public" starts to use mnm.
4. When it reaches critical mass among general population, e-mail can start to be phases out.
Don't know how realistic is this, and some design decisions of the mnm team seem counter-productive, but to me it does not sound completely crazy.