Yep, my key insight was "oh, you don't worry about next month". So you just need to separately know when the current month ends (whether a leap year, etc), so it's a pure series of seven day weeks starting from an arbitrary offset. Really elegant, if a little daunting that my entire life will be described by that rectangular frame twitching backwards and forwards across a field of indistinguishable dates :-)
It presumes you know both what the current month is and how many days it has. I'm pretty solid on the former and for the second it's either "thirty days hath September" or counting across my knuckles. I also know it's Wednesday but don't ask me whether it's 28 or 29. That's where I'd be checking a calendar.
But it is something of an exercise in minimalism, sitting between functional and fun. So not for everyone, but scratches my itch, as does my wall clock with just an hour hand smoothly gliding through the day (it has 12 marks per hour so at a glance one sees the time to a resolution of a few minutes, which is more than good enough for almost anything in daily life)