On the weekday names we are not doing any better. Tuesday - named after the god of war? Doesn't make sense to me.
As for the lengths of the months, imagine if you were trying to make the case for the different lengths of months and you were trying to get buy in from your friends in accounts. Surely they would want equal amounts of days in each quarter? Imagine trying to persuade them that different lengths were better, what plausible possible reason could there be?
We learn the names of days and months by rote at a very young age. We get encultured into accepting the status quo and never questioning little details - nobody asks at school why 'Dec'-ember is month twelve.