To be honest, I'm mostly joking about the billionaire thing. If I were emotionally invested enough in this idea above other parts of my life I would look for a way to get it moving. The problem is that, by its very nature, a non-profit open-source project like this could not attract venture capitalists or angel investors, lest it become the very thing it was created to challenge (*cough cough*, OpenAI, *cough cough*). A project like this would need venture altruists or angel donors instead to be feasible and sustainable — hence my fantasy of become stupidly rich to be able to get it moving, at the cost of downgrading to "normal rich".
You don't need investors, unless you think you can't get users without buying them. The platform you described don't need much resources and can be bootstrapped. You can still capture just 1% of the value that Match Group captures and live nicely.
I think the reason we don't see competitors like that is that dating without aggressive monetization won't be much better for the average user.