This has nothing to do with leap seconds. Leap seconds are the worst mechanism in keeping time, there's not a single advantage to having leap seconds.
> A day is defined as the rotation of the earth around its axis.
And we can now measure time with precision high enough that tying to Earth's rotation is not acceptable. We can still use timezones to fix the shift.
> Changing any of these will make the summer drift into the winter, or the night into the day, or whatever.
Yeah, and it will take a millennium for Earth rotation to shift enough for people to notice it. On the other hand, you'd have no problem with summer/winter time I presume?