The central server cannot connect to the each door without Ethernet and TCP/IP. If the server has to communicate with every single door it has to use Ethernet and TCP/IP

Sure they can. They just use something other than Ethernet and TCP/IP.

You need to go do some serious reading about what they are, what they aren't, and some of the alternatives that exist.

 

There are other options, such as Bluetooth, Zigbee, CAN bus, I2C, optical, and the list goes on and on -- and that doesn't include ad hoc and/or proprietary connections.

If you think ethernet is the best option for your system, then use ethernet.

 

Ethernet would be used for local communication between the smart devices and the central controller, while TCP/IP would be used for remote communication between the user's smartphone app and the central controller.