Why do the number of days in a month vary: 28, 29, 30, 31.

Let's make each month 28 days, and add a new month with 28 days after December. We'll call it Mondoember.

Every day of the week will occur on the same day each month.

That all adds up to 364 days. To accommodate the 365th day in a year, and the extra day in leap year, every 7 years we will add 1 week to December to lengthen the Christmas Holidays. Periodically, we may need to add another week here and there to keep synchronized with Earth's revolution around the Sun.