RAX 40 range improvement

Theoretically the router probably could cover that area. As you've found out, practical application is a no.  Many different factors influence this from building materials, types of insulation, where the router is placed, hvac runs, layout of the house, etc. Under optimal condions, it'd probably work. I've got a 3200 sqft house and use an orbi with 2x satellites for full coverage. I've tried a new AX router and the Orbi was still faster and had better coverage.  So I went back to Orbi for now.  Yes, the new ax specs has a slight extra range but I doubt any of your devices (maybe 1 or 2) actually have ax built in. 

4000 sqft is what I'd consider a large house. If your still in the return period, I'd look at the orbi setup or an equivalent mesh setup with a satellite or 2 to fully cover your house. Especially if you've got a gigabit connection. A single router in that large of a house will struggle even if you're running the new RAX200.