Right, there would still be a need for a day or so extra at times. Would make nice holidays.
And the moon cycle would not start on the annual cycle anyway. Dunno what you can do about that. Muslims just gave up and let the new year keep shifting throughout the solar year so that months are exactly aligned with the moon. The Jewish calendar is insanely complicated. So maybe it can't be done in any reasonable way.
We could also get back to sane naming of months. Sep - Dec always bothered me. I know they were literally the seventh to tenth months in the Roman calendar, but now they are not.
#humor