It's more complicated than that. Everything that calculates differences between two points in time for example would need to be updated to know about when the switch occurred. And more generally, this is an example of why it's complicated - because it's easy to overlook things that could be affected, so there's a great deal of investigation and testing that would need to be done.
Many systems that are in production have no regular release schedule, may go decades without any changes to code, and they have no maintainers.
The delay is for those cases -- where someone may need to be hired to fix it, or an entire system may need to be replaced if it is no longer maintainable.
Sure the actual change might not sound super complicated, but hunting down all the little machines, services, and ancient code isn't easy for all organizations.
Most people don't that though. They use databases, system and apps that implement their own logic for time changes. Maybe you need an OS update. Maybe it's code that is controlled by a third party. There's plenty of logistics necessary to make sure things don't break when the DST rules change.
