Sure, we will randomly move the end of the DST from the last Sunday of October to the first Sunday of November and everyone will try to kill us, right? DST is the perfect example that we have a relative freedom in changing time zone offsets.
You are however right that this is a political matter requiring some (but I believe, reasonable) amount of coordination, but timekeeping is in many parts political anyway. Practically speaking countries would implement the change out of necessity and not because of agreements, as one hour deviation is significant enough.
> we have a relative freedom in changing time zone offsets
Who is we in this sentence? Programmers certainly don't, they have to report times and timezones in their software as the populace expects it to be reported. Governments can change timezones, but they're not going to, because the political cost of telling everyone that they're in a new timezone is greater than the political cost of telling programmers where to shove it.
Most of the public will see absolutely no reason why they should have to permanently change the timezone they're in for the sake of a one-time event. And honestly, even as a programmer who'd be doing the fixing, I agree that they're right.
Governments absolutely can. The updates to tzdata [1] are full of arbitrary changes happening all around the globe, not just for a few weird countries. The example I quoted above is 2007 changes to the United State's DST and a perfect example that governments can push time zone changes with at most marginal perceived benefits. Also remember that the current proposal to abolish leap seconds itself was primarily arosen due to computing complications anyway. Programmers can (indirectly) affect the future of leap seconds than probably any other group else.
Russia decided to just stay on DST with 6 weeks notice a few years ago, thereby instantly creating half a dozen new timezones. And now they're discussing going back to normal time/DST...
You are however right that this is a political matter requiring some (but I believe, reasonable) amount of coordination, but timekeeping is in many parts political anyway. Practically speaking countries would implement the change out of necessity and not because of agreements, as one hour deviation is significant enough.