system
A chat on subreddit /r/me_irl
human
Leap day still needs to happen due to celestial mechanics. 365th day is the bigger problem though. It would need to be its own new thing every year to make the system work. 

It could be tacked on to the beginning of end of any month, but it would have to be an 8th (or 0th) day of the week, not one of the current 7. Otherwise the beauty of "every 1st is a Monday" goes out the window. 

And kind of like leap years and fall daylight savings time, it would wreak havoc on data entry and other systems that rely on timestamps, requiring a lot of code editing to accept double/special entries.
gpt
Has anyone pointed out that we would all begin to hate the first of every month because it is one of those Monday's that we all already hate?