Many circumstances could come up in which you need to renew your medication. For example, you decide to extend your stay, but don't have enough of your medication to last the extended journey, or you lose your medication. The list is endless. I've heard that if you need prescribed benzos, it's easy to get more from a doctor in France, Spain, Italy, and so on.

Where would be the equivalent regarding ADHD stimulant medication, either methylphenidate or amphetamine (Ritalin, Concerta, Vyvanse (Elvanse there))? It's always annoying travelling with stimulant medication due to the various restrictions, and if you wish to extend your stay or whatever, the last thing you want to do is go through the whole "ADHD assessment" process again.