they won't bother telling you the frequency
They don't always know what you're going to do next, so they might not be able to.
Furthermore, I hope I'm not the only one creating a list (either mental or on paper) of all the frequencies/facilities I'm going to use during a flight. So when I'm leaving the info frequency because I'm going to enter into controlled airspace, or cross a FIS boundary/border, I already know what my next frequency is going to be. (In fact, I usually have it selected as the standby frequency by that time. But that's just me planning ahead.)
And if due to a change of plans I need to find a frequency, well, that's what the info frequency is for. If I can't find it quickly enough on the map, that is.