GoKawiilBluetooth handles two specific jobs when it comes to wireless Android Auto: the initial handshake between phone and car and hands-free calling. The handshake is what kicks off the whole process. Bluetooth, as a technology, is energy-efficient and low-power, so your phone can scan for your car's system in the background, pair the two, and exchange the credentials needed to launch a Wi-Fi connection. The only thing you have to do is to turn on your car.
Handling hands-free calls is Bluetooth's second job in your car. Android Auto routes audio through your car's speakers using the Hands-Free Protocol. If you disable Bluetooth during your drive for any reason, it simply kills the connection. For these two reasons, you can't run wireless Android Auto without Bluetooth.
As mentioned, Bluetooth also launches a Wi-Fi connection. So, why does Android Auto turn on Wi-Fi? Because Bluetooth tops out at around 2-3 Mbps of data throughput. That's enough for audio alone, but definitely not enough to stream a high-resolution map interface, audio and touch inputs.