Wouldn't it make more sense to start seasons around the 1st of a month instead of the 21st?

It would make things simpler to have winter, spring summer and fall start on the first days of January, April, July and October. I suppose nobody else is much concerned about this, since I have never seen it discussed anywhere. I did a Web search and found out that the 21st was chosen so that Easter would fall around the beginning of spring I don’t mean to offend any Christians here, but is this really important? If Pope Gregory had removed a few more days from 1582, he could have had things lined up so that they make sense.

Something else I thought of. Might this be related to the start of the astrological calendar divisions occurring around the 21st also?