Why Not March Fools' Day?

A belated happy new year to y'all.

At this time of year I always end up musing about the months of the year and why the new year starts where it starts. To be honest I don't get New Year's Eve, it doesn't have the same natural vibe that Christmas has and it always feels like a forced celebration to me. Consequently I always end up arguing with friends and family that it would be much better to have it sometime in spring - the natural beginnings of things.

Looking at the calendar March 1st seems like a natural break point. Apparently March was the first month of the Roman calender and this is said to be why our calender looks so fudged when we contemplate the names of the months. They supposedly had ten months originally and then added January and February later on. Logically, January and February should be the 11th and 12th months, but for some reason they come at the start of our year.

September - septem means seven in Latin yet it's our ninth month
October - octo, eight, yet our tenth month
November - novem, nine, yet our eleventh month
December - decem, ten, yet our twelfth month

Also, to me, the fact that February contains the extra day in a leap year also makes it a more logical twelfth month - it makes sense to add the extra day to the end of the year, rather than at some random intersection between two months.

Anyway, this led me to wonder why not March Fools' Day instead of April Fools' Day. Looking at the conventional explanations for all this calendar mayhem on Wikipedia etc it kind of looks like April Fools' is pretty much a consequence of the new year beginning in March (sometime). Although what with all the various local traditions and the changes from the Julian to the Gregorian calendar it gets pretty confusing. I feel a bit like I've wandered down a rabbit hole.

(The traditional quarter days seem like an interesting thing to look at next. Also the name Gule of August caught my eye - another name for Lammas. Gule - yule?)

Oh and before I forget, going back to the Roman months I've always found it odd that the months of July and August were renamed for Caesar and Augustus. I feel the worship of these two blurs into Christianity somewhat.  Anyway, I was wondering if maybe August shares its root with the Latin word aurum meaning gold. It would be quite fitting for a summer month and also the name Augustus was a title used by many emperors (likewise Augusta for empresses) - maybe it simply meant golden one. An augur in ancient Rome was a religious official or priest.

Also an aureus was a gold coin - so maybe a link to the person depicted on the coin. I think the Latin word chrysos means gold too - Christ? Do Augustus and Christ mean the same thing?