Did you know that calendar reform was seriously considered at the beginning of the 20th century? Proposals similar to the one above were were actually getting traction in the interest of efficiency during the Industrial Revolution. There were many combinations of proposed changes endorsed by various groups and individuals, but the one above — the most radical overhaul — was the most logically elegant.
Ideally, as this line of thought goes, the year should be divided into 12 equal months of exactly 30 days. Each date would fall on the same day of the week every year, and every quarter would start on a Sunday and end on a Friday. There would then be a special holiday at the end of each quarter, which would be designated as a Saturday, but not part of any month. Immediately after the June holiday, there would be an additional holiday (usually called “World Day”), which would be neither a day of the week nor of any month. In leap years, Leap Day would be in essence an extra World Day at the end of the year. The one quarterly calendar above would be sufficient for the whole year, year after year. These extra dates could be written and accounted for with “Holiday” as the month, and numbered 1-5 (1-6 in a leap year). Sure it would be odd to have extramonthly and extraweekly days, but would having a birthday on 6/Hol/56 really be any more awkward than 29/Feb/56?
Unfortunately, the momentum for international cooperation was somewhat deflated by a little thing called the First World War. Furthermore, conservative Jews and fundamentalist Christians were among the biggest opponents of these proposals, because they felt that having days that fell outside of a 7-day week was in opposition to the 7-day sabbatical cycle God laid out in Genesis.
In any case, it’s all water under the bridge. Nowadays, so much automated computer software has been coded around the existing Gregorian calendar that the idea of a new system is neither practical nor as desired.