In fairness, July and August weren't inserted, they were renamed from Quintilis and Sextilis, literally the fifth and sixth months of the Roman calendar.
Much earlier, Pompilius (history about whom is largely legendary, and actions attributed to him should be taken with a grain of salt) introduced January and February and set the numbering out of line. These months were previously just lumped in as monthless winter days.
All Julius Caesar did was rebalance the calendar without changing the months. The rename of Quintilis was posthumous.
Gregory XIII then further tweaked it to give us the modern calendar.
Not until quite recently there was work to be done by the masses during off-season. We used to semi-hibernate. There are still some communities that do.
If those months weren’t months and everyone just assumed it was a wasted timeslot, everyone would be happier.
Humans are not meant to work 40/50 (We are meant to work 20/40 - 20 hrs 30 weeks a year) hr weeks 50 weeks a year