But they wouldn't, because the lunar cycle isn't 28 days.

https://en.m.wikipedia.org/wiki/Lunar_month

Lining up with the solar cycle / journey is more useful though (away from the equator at least). I suspect that is why people landed on a ~365 day calendar.

The one extra day a year would mean the full moon would fall back by 1 day every year relative to the months. Which still would still be pretty handy.

The lunar cycle is not 28 days, or even a whole number of days.

if our orbit around the sun was a perfect circle instead of elliptical we could ignore the orbit completely, or at least I would be willing to, and focus on the moon or just some interval of rotations - day/night cycles

Winter/Summer cycle is more about the angle of Earths rotational axis and not the distance from the sun.

Handy for what?

Most civilizations started with a lunar calendar (still used in Chinese and Islamic calendars), because it was much easier to observe the lunar cycle than the solar cycle. The solar calendar was the more useful one for getting good harvests, but technically much more challenging (requiring several tweaks over may centuries get the calibration right).