Ideally and on paper, that's the very perfect situation. But practically, it's not easy to boot-strap enough liquidity. But I do believe that the more trustworthy and influential members of the BitcoinTalk community should organize us plebs and run a coordinator.
Yes, that was the part I missed adding to my reply. With BTCPay server it seems to be a very simple procedure to set up but the key component that will make the coinjoin both possible and feasible is going to be liquidity. Maybe with a little bit of advertising and promoting it can attract enough people to the service but without liquidity the coordinator will fail.
Plus the community should probably run more than one in my opinion. Some of the services that are advertising in the forum should probably be involved as well.
Did you have any names in mind?