We already accept an error of half an hour (most timezone offsets are multiples of a whole hour) or more (many timezone boundaries are widened to align with state or country boundaries). A couple of minutes is nothing next to that, and if start getting too far, we can simply redefine the timezone offsets (which we already do twice a year in many places, and any device which might be moved across timezone boundaries already have to deal with that).

Also, historically, we did care about the equinoxes and solstices falling on specific days of the calendar.

We may not care anymore, but emphasis on may.

And you can still use UTC as your indicator for day and night. In 100 years, it would only drift around 1 minute.

We don't really do that on a second accuracy though. We need to add a whole new day to the calendar every four years to make up the difference. Meanwhile we've added less than half a minute worth of leap seconds.