I believe the service, as per Microsoft own calculations, is profitable.
I mean, people here want them to factor first party dev costs, but I don't think it should work that way from a business perspective.
What really matters is if first party games weren't at the service, people would still sign up to it, and if the gamepass revenue is enough to justify cannibalizing some (or most, like some folks here like to see) revenue from first party studios.
People here have conjectured that the revenue from studios is severely handicapped by the gamepass lending some of those games to the service, and if gamepass had to pay to first party studios like they pay to third parties, the service wouldn't be profitable. Some here even think that if the studios were payed in a "fair" way, gamepass wouldn't exist or some canceled games or closed studios could have a different fate.
I have another view about it. I think that, without the service, Xbox Series would be as dead as WiiU. So, it wouldn't matter if the split is fair or not, if the people aren't invested in your platform, it will eventually die. Simple as that. Maybe the Xbox and studios management aren't good enough to put good titles in a consistent way that only games are enough to keep the platform afloat. And that is a management problem, not gamepass one. Maybe gamepass and a gigantic publisher acquisition are the only way that Phill and co. could come up to keep the platform alive. I also have saw other hardware manufacturers step out of the market and none of them dare to go back in the industry to fight against the giants again and that is why I believe that isn't viable to just call Xbox a day, reorganize, and lauch again in another time. So that's why they would try everything in order to keep Xbox alive.
So, in the end, it simply isn't productive to discuss if a service is profitable or not, or in what metrics, when the very same company havr stated that it is, no matter who have said. That is, unless, some have presented proof that the stated isn't true.
In the end, the very service most of you here have accused of being the defeat of the platform, could be the very thing that is keeping your beloved Xbox afloat till now.