This is kind of the part giving me pause. Surely if you tie the service to the console, then both are bolstered. They reinforce each other more easily that way.
Gamers and film/TV buffs may intersect one and the same (obviously), but a single person can still view the two realms differently. Film and TV have been hardware-agnostic for decades, same as music. On the other hand, gaming software is still mostly hardware-bound; you need a certain console to play certain types of games. I think most console gamers are going to think the same of gaming services for a while so there's a chance they are pushing Gamepass as a hardware-agnostic game service defined through the Xbox console brand too early. Maybe half a decade too early, in fact, going by how long it took for digital game sales to go mainstream compared to when MS were trying to push that with XBO (2013 vs. 2018, roughly 5 years).
Guess we'll find out soon where MS are going with this but at the very least it doesn't seem like the sort of thing a company seeking to remain a main platform holder would be doing. There's even some historical precedent here; SEGA, SNK, NEC, 3DO etc....when these companies started somewhat more heavily pushing their games to other platforms (SEGA starting SEGASoft and publishing Saturn games on PC, SNK publishing Neo-Geo games on SNES/MegaDrive and then PS1/Saturn/3DO, etc.)...not too far later they would transition to third-party.
We could be witnessing that with MS right now and I wouldn't be too surprised if they do in fact go third-party within the next 3-5 years, but in their case moreso out of choice. Maybe their recent platitudes and messaging could be a result of discussions with Sony and Nintendo people towards that type of inevitable future. Just imagine how big a benefit MS would get by having Gamepass and xCloud on Sony and Nintendo devices...but that would mean them needing to give something out. Downshifting focus of Xbox as a console brand would be such a thing to scale back to make that happen.
I actually could see a 3rd-party future working brilliantly for MS; they have the internal studios (Coalition, Playground, Turn 10, Ninja Theory, Initiative etc.), they have a service platform to give value benefit to those games, they already have successful 3rd-party ventures on other platforms (Minecraft, Sea of Thieves, Grounded potentially), and they have more money than any other company in gaming except Google (who isn't taken seriously among the core gaming market anyway) and arguably Apple (same).
As a 3rd-party they could definitely be massive, potentially moreso than EA, Ubisoft, even Rockstar. The question is how will they manage this type of transition and how gracefully will it be for those of us in the Xbox community. That's a key component, and a lot of it is going to rest on how they handle Series X (and Series S).