This is because Time::Piece doesn't care as much about timezones and DST.

Precisely so. That's another good reason to use it in this sort of scenario where DST is a hindrance at best. I don't see why, given a problem where DST and timezones would only complicate things, the user would choose a non-core module where these are important over a core module which for the most part ignores them.

For the general audience reading this, if you are used to DateTime or Date::Calc or any of the myriad other modules, I do recommend that you become at least passingly familiar with Time::Piece. It is pretty simple, fairly lightweight and core. It won't solve all problems but it handles a good subset of them, including the one in this thread, very well indeed.