I prefer to use HTTPS when I can. More and more sites force HTTPS and this is right.
Moreover, recent I read that Firefox wants to make HTTP outdated, definitely, in long term, but still.
So, can I use HTTPS for web interface of my Synology NAS? Yes, I can (at least in DSM 5.X), but this is not a default option (what is strange for me, btw).
Following screenshot shows how to enable HTTPS in Synology NAS. This is a single screenshot, so it is really easy to do.