Is it important that midnight is actually midnight? I don't know. I would prefer it to be, but perhaps I can just update my knowledge on when the midnight actually is once or twice a year. Perhaps it isn't a big deal at all. But I wouldn't dare to claim that "surely there can be no problems with it".
And, yes, that kinda means I don't support the leap second removal. It wasn't great, but eventually fixing the software written by incompetent people sounds more like a solution, than breaking the existing solution and making both competent and incompetent people alike eventually come up with a new one (to abolish it as well after 100 more years).
Midnight is almost never at midnight.
Let's talk noon, specifically solar noon, as it is easier to visualize. Solar noon varies throughout the year, and based on the position in the timezone.
Solar noon for two cities in Eastern Time Zone: 11:29:16 - Boston 12:22:36 - Atlanta
Tomorrow, solar noon in Atlanta will be 12:22:50, 14 seconds later than today. No one notices a 14 second shift from one day to the next. As you can see, solar noon is almost never at clock noon, yet no one complains about that. Who would notice a 1 minute shift over 100 years?
The programming problem is made vastly more difficult because the leap seconds are not known in advance. When a new leap second is announced, every dependent system has to be updated.
