EAC already supports Proton, albeit recently, [1] and BattlEye supports Linux and macOS natively already with Proton support in the pipeline [2].
It's not impossible, it's just up to Activision.
[1] https://dev.epicgames.com/en-US/news/epic-online-services-la...
[2] https://twitter.com/thebattleye/status/1441477816311291906