> so we could stop it without breaking anything
Well, until some sufficiently influential government or organization gets annoyed with the discrepancy with solar time and comes up with their own correction to the local clocks under their jurisdiction. Then at the bare minimum you need all the commonly used date/time libraries to be updatable with this information. Existing solutions like the tz database [0] might already technically support this, although I have to imagine that the logistics will be annoying at best.