I'm fairly sure Microsoft doesn't even have the ambition to make it profitable. Like Youtube for Google, or costco hotdogs, it's to get a foot in the door (or rather, customers' feet in your doors) to upsell people on all your other products.
The infrastructure to store and deliver seamlessly zettabytes of video all around the world surely doesn't come cheaply.
Though Google is likely doing accounting shenanigans with cross-company billing and charges YouTube "just enough" for the datacenter/cloud access that, on paper, it's barely breaking even (if only for tax advantages). But I don't have proof of that.