A really great feature, that would set Thunderbird and K9Mail (Thunderbird for Android) apart from all other mail clients: The ability to sync contacts and calendar on multiple devices without any external service provider ("cloud"), without using any internet connection, just on the local network, when both devices are in the same LAN (WiFi) for maximum data protection.
I would image it like this: The user can open a dialog/page with known devices for synchronization. The user is able to search for other Thunderbird installations in the same network and will get a list of devices and can add them by clicking on it. Both devices will exchange keys and will both display for example the same 6-digit code, the user can compare these codes and them click accept on both devices. The keys will be stored in both installations and the devices now know each other. The user can now configure what should be synchronized in which direction with each device. Synchronization will be performed (if possible) when data that is synchronized is updated. If the other device is not accessible it will be checked periodically.
How I image it on a technical level: Thunderbird will open a IP port for receiving messages. Each installation/profile will generate a public/private key pair. To init a connection/search for devices a broadcast message will be sent containing the hash of the own public key and either the hash of the other devices public key or a search for all devices. Other devices will answer with the hash of their public key. The data transfer is then done directly to the then known IP address. This way changing IP addresses are not an issue (the user doesn't even have to know what IP addresses are), all devices are equal (no server/client differentiation in Installations) and it is completely OS-independent.
I use Thunderbird since version 0.5 (that was Februar 2004, just checked my outgoing mails) and I love it has been a reliable piece of software ever since. I also use K9Mail since I got a smartphone. IMHO this would be the best new feature since almost 20 years.