That said, I think months may just be one of those terrible systems that are too ingrained in our society.
I still wish we could do 13*28 + 1.25 days, thirteen months with twenty eight days each, every month starting on a Monday, with a special 'festivity' day at the end of each year, sometimes 2 days. That would work a lot better I think, but because of proud Roman emperors, we are learning and working in one of the worst arrangements possible.