Why are the days of the months not more evenly distributed?

There are 7 months with 31 days
There are 5 months with 30 days
And there is the odd one out with 28 or 29 days

To me it would make sense to have:
6 months with 31 days
5 months with 30 days
and February with 29 or 30 days. It would balance out better

We have 'corrected' time with "daylight saving time". Why not with our calendar?

Anonymous2010-08-09T03:28:47Z

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Daylight saving time is not intended to "correct time". It was first proposed to save on candles, by moving all activities further ahead so they could make use of daylight when the days were shorter in winter.

The days of the month are not evenly distributed because months are vaguely based on the movements of the moon, just like years are based on the movement of the sun. It is leap days that "correct" time, by adjusting for the fact that a solar year is not exactly 365 days but slightly longer. Without leap days, the months would move so that they no longer corresponded with the seasons (e.g. December might end up in spring)