As someone who would play on Linux then, it doesn't sound like a solution at all. The separate version would just be filled with cheaters then, would almost be like an punishment for Linux users.
That way you don't need a backdoor in the Windows version of the game for the weaker Linux anticheat that runs through Proton. You would just have a native Linux version of the game with native anticheat.
But EAC has a kernel driver and there's no real native way of doing that on Linux that's stable as Linux has no stable kernel API, and measured boot isn't widely adopted so a custom kernel can just lie to the anti-cheat module.
I really hope Valve work on this, whilst it would mean perhaps online play only run on SteamOS in an optional locked down mode, it's better than the status quo.
This is exactly the problem. Users connecting via Linux are more likely to be cheaters, since the anti-cheat is weaker on Linux, so in order to protect the user-base at large (Windows users), they don't allow Linux clients at all. Allow the less protected Linux clients to connect goes against the very change they did.