Should Marketing Designers and Product Designers belong to different teams?

I've just joined a SASS company as Head of Design in which I'm leading a team of Product Designers. I learned after a couple weeks that there are also designers under the Marketing team who seem to be treated as pixel pushers for Sales and Marketing, creating sales docs and making small changes to the marketing site. Basically an endless stream of requests from Sales.

I'm thinking of pushing to create a Design structure at this company in which no designer reports to a non-designer and we can create shared design goals. Essentially, all designers, regardless of specialty, would belong to my single Design team with shared goals and be embedded in different teams, such as Marketing. This way I can have my designers' backs, we can easily learn from and collaborate with each other, and we can tackle the entire platform in a more holistic way.

Does anyone have any experience with the structure I'm proposing or see any holes, red flags, etc? I'm also curious of any particular examples of this structure. Politically, this is pretty tough since it can be seen as stealing resources so I need as much ammo as possible.