I like the idea for a variety of reasons but can't see a path to it.
Phil Galfond's site was launched with a lot of fluff regarding the player experience but that hardly disguised the fact that it was for profit. The subsequent Galfond challenges were launched due to the fact the site had drawn little traffic. Though large sums were invested at the outset, the costs and challenges meant the hard launch was delayed and the variety of games offered was limited.
It might sound absurd but the only way I could see this happening is if a golden benefactor decided to sponsor such a site...but would they then after such investment be content to allow the fans to run it themselves?
However as a side note (as you touch on RNG) I will mention Replay Poker as alternative playing experience. Yes, it is for profit but runs with play money with over a million members (and is obviously affiliated with CC regarding promotional events).
I turned to Replay when learning/building my game after enduring an extremely frustrating phase elsewhere, and have noted (as others) that their RNG appears to be truly random. Though the site is expansive it seems the core personnel are fairly small (presumably paid) with a lot of site monitoring done by members who volunteer their time (akin to CC).