Maybe here's an example that's more useful: Some years ago, I worked on an in-house IaaS platform that included several workflow modules for the sysadmins (alert dispatching, time-tracking, etc.).

One of those components was a scheduler for one-time and recurring tasks. For example, when you delete a system, you set a timer for 14 days to have the system remind you (via e-mail or by issuing an alert into the queue) to delete the system's backup. There were also a lot of recurring tasks that needed to be performed daily or weekly. Now if you have a task thats configured daily at 9 AM, it's tempting to implement the timestamp series as

  while (true) { timestamp += 86400; }

And indeed, that's how it was done in the existing code. But that means that once DST starts or ends, your daily-at-9-AM-task suddenly happens at 8 AM or 10 AM instead. Whether that's a problem depends on the type of task and how the sysadmins organize their work. And then there's the monthly recurrence, which is even messier with plain timestamps.

I cannot recall all details anymore, but I definitely remember that twice a year, after each DST change, someone would go through the list of recurring tasks, and move the times forward (or backward) by one hour manually.

EDIT: Maybe the simplest (though not easiest) solution to the irregular month lengths would be to attach giant thrusters to Earth and push it away from the sun a bit, so that our year is 366 days instead of 365 long. Then we make a calendar with 6 months per 61 days. As a bonus, it would reverse some of the effects of global warming. (Alternatively, go to 368 days and have 16 months with 23 days each.)