What's the nature of your operation? If they're not giving you money then you're within your rights to say "sorry, don't use outlook"
Usually they are giving you money...
I ran a SaaS up until recently. Emailing users notifications for events was just a normal part of the app. Users got upset when the emails didn't come through. So then I had to be email tech support for something I had no control over. Lovely.
Our customers are giving us lots of money. And the nature of the emails are account reminders, activation and internal message notifications.