I read in computer security book that there are three places in wireless networking where you can be attacked: wireless transmission, access points and wireless network itself. The book illustrates that eavesdropping may occur during data transmission and the countermeasure is encryption. On the other hand, for access points, the main threat is unauthorized access, which is handled by IEEE 802.1X (authentication). Assume that hacker accessed the router, let's say bruteforced passwords. So, it is confusing, why do we need to encrypt the data if an attacker has already got access to an AP? Even if the wireless transmission is encrypted and data received by a router is violated, and as I know, information cannot be processed in ciphered format, it is needed to be decrypted first and then processed. So, why do we need to encrypt data against eavesdropping if threats come from different side?
Having access to an AP doesn't mean you get to see all the data going through it. You'd have to gain admin access, then tell the AP to send all raw data to your device as well. That's a lot more complicated than it sounds. The danger of AP access is that a hacker could try to use SMB or other protocols to access your files. The network data itself is still isolated from you without either a firmware update or custom settings that many AP don't even offer to begin with. Having an unencrypted Wi-Fi connection only makes it easier to see unencrypted (e.g. HTTP/telnet) data. You still wouldn't see HTTPS/VPN data, because there's another layer of encryption.