Fyi there are 365.242374 days in a year.
I’m not an expert on the subject, but at least one of the calenders you’re thinking of is a Lunar calendar.
So not 365.242374 days but a variety of other synchronisation problems.
This mess pops up every time that we’re relying on multiple primary standards for the same property (in this case, time). If redoing it, it would be simply better to use the day as the “one cycle to rule them all!”, and then use exact and round-ish multiples/divisions for larger/smaller amounts of time. (e.g. “a new-second is 1/80000 of a day” [currently 86400], “a new-year is 400 days”)
…except nobody is touching some weird shit that has been ingrained in human societies for a million and half of days. Probably even before that.
Having summer and winter start around the same time every year is a pretty good thing to have.
It is. But I think that having rounder numbers is even better - it simplifies any measuring, division or multiplication. People planting crops/etc. would likely refer to the seasons instead of year (same as now), and school summer vacations would be likely set up per year (just like Easter etc.).
A somewhat middle ground approach would be if the “social year” was defined to have 360d. Seasons and years would still mismatch over time, but from one year to another they’d be rather close. (e.g. if summer started 10/Mar this year, it’ll start ~15/Mar in the next year)