Do I really need an elevator in my hostel?

Elevators can be quite expensive. The installation and maintenance costs will not be small, and the loss of communal space is important. If it does break down, then guests will complain that it's there but they can't use it. In the other scenario, if there's no elevator, then you can enthusiastically agree when they say, "I wish you had an elevator." A concurring "Me too!" is much better than an apologetic "I'm sorry."

An elevator is not necessary (unless required by law) but your guests on the 6th floor will definitely appreciate it. Especially those with heavy rolling suitcases instead of backpacks. If you have staff members willing to help carry the bags up, then the importance of the elevator is greatly reduced. Those helpful staff members will probably get tired of hauling suitcases up six flights of stairs pretty quickly though.

Ultimately, if you can afford it and it doesn't take up a ridiculous amount of space, then I'd say it's a worthwhile investment. If you can't afford it or if it would really limit your common space, then you can go without. If you have a great atmosphere, then your guests will forgive the extra exercise.

Along those lines, I saw a a great idea in a hostel without an elevator. On the stairs they painted "10 calories burned" "20 calories burned" and so on all the way up to the top floor to put a positive spin on the situation as their guests climbed. I also remember a fellow backpacker who repeated aloud, "nice legs, nice legs, nice legs" to keep positive as she climbed long staircases.