We should have 13 months instead of 12. If we had 13 months, every month would be 28 days a.k.a 4 weeks, it would always start on Monday and end on Sunday, all celebrations would be always a fixed date, we would align to the phases of the moon and kalendars would become obvious. The additional month would be called Sol, for the sun.
If someone said 1st of June, you would always know they mean Monday, and if someone said 3rd Tuesday in February, you would always know its 22nd of February. No more irregularities. Every month the same length, every calendar the same structure.
The benefits of a calendar system like this are immense. It is estimated it would save billions of $ on the effort of time calculations worldwide (and the mistakes from confused dates), but its not just that. It would reshape the culture.
Some folks would say it is impossible to reshape how we do the calendar, but please realise we already use the 52 weeks system in professional settings - many account the time by saying "Week34" or "W45". This is just 13 month calendar which skips the Months.