Thank you for your answer Igor!
Actually I'm on a fresh install (just to be sure none of my previous experiments might have affected the outcome) and yet I alway get the same behaviour: the MOTD is shown just upon first SSH Connection after a reboot, then every other time I got the simple "Last Login" Info.
I'm only able to reproduce the MOTD by issuing the followwing, but It's quite annoying to pass this command each time I want some information:
cat /etc/motd
I'm using Bitwise SSH to access my Debian machine, and I'm starting to wonder if this is the cause of the strange behaviour....