I get where you are coming from but this just feels like a semantics argument. Just because it’s called marriage in both venues doesn’t mean it isn’t already functionally exactly the way you put it.

It feels like a semantics argument because to a large extent it's a fight about semantics. Most of the people opposed to gay marriage aren't fighting the idea that gay folks should be able to see each other in the hospital, or be covered by each other's insurance, etc - they're fighting the idea that their religious ritual from their homophobic religion should be required to accept gay people and/or that they should be required to accept gay people as being in the same spiritual state as them as a consequence of their ritual. It's why arguments against gay marriage are only extremely rarely about the legal rights and privileges granted by marriage but nearly always about things like "sanctity."

Fully separating the legal and cultural/religious concepts of marriage, including in the language is meant to resolve that by ceding the semantic ground without having to cede any actual rights. You qualify and fill out the paperwork? You're in a civil partnership. Do whatever rituals you want, argue whether or not each other's rituals "count" all you want, everyone gets the same rights legally and the government is not in any way saying your rituals are or are not equivalent to anyone else's.