Scene one: the broke student facing exams, where the duration of a trip is never just a matter of cost.
Of course, low season is ideal for the wallet, with softer accommodation rates, but the academic calendar doesn't always bend to good deals.
I've already missed crazy offers because my exams fell right when cheap tickets were available, or I had to work to pay the rent.
Sometimes, a short stay in peak season, like a weekend in Berlin for a festival, is worth more than a long boring week off-season, even if it costs a bit more at the time of buying train tickets.