This is just a Lunar calendar. There is a reason we don't do Lunar calendars. You desync with the rotations around the sun. The muslims do this and this is why Ramadan is in different seasons all the time. Ramadan slides around the seasons because the Lunar calendar is not synced up to the rotations around the sun and so one year the month of Ramadan is in summer and a decade later it is in winter.
Our strange system of months of 30 or 31 days with February at 28 and sometimes 29 was invented to make sure January is always cold, and July is always hot (in the northern hemisphere). We figured this out around 500 years ago but people on the internet think of the old system we used to have and got rid of because it's bad and go "OH WOW THIS WOULD BE SO SMART".
Sorry for ranting about a meme I know it's just a haha but I think people genuinely might get the wrong idea that this would actually be good.