I am very much used to these kind of questions. Are 2-categories useful? What can one prove using gerbes? Why should I care about stacks?

I think a funny way to react to these kind of questions, with often surprising results, is to return the question:

If you want to know what higher X is good for, explain first what X is good for, in your opinion.

And whatever the person answers, I found it mostly very easy to generalize the given argument from X to higher X.

Example 1 If X is "category", a common answer is "it keeps track of the automorphisms of the objects". Well, a 2-category keeps track of the automorphisms of automorphisms.

Example 2 The question was: "What can you prove with gerbes?", so I'll reply: "What can you prove with bundles?". People are often completely puzzled by this question, so they'll accept that a notion may be useful even if they're not there to prove something.

I am very much used to these kind of questions. Are 2-categories useful? What can one prove using gerbes? Why should I care about stacks?

I think a funny way to react to these kind of questions, with often surprising results, is to return the question:

If you want to know what higher X is good for, explain first what X is good for, in your opinion.

And whatever the person answers, I found it mostly very easy to generalize the given argument from X to higher X.

Example 1 If X is "category", a common answer is "it keeps track of the automorphisms of the objects". Well, a 2-category keeps track of the automorphisms of automorphisms.

Example 2 The question was: "What can you prove with gerbes?", so I'll reply: "What can you prove with bundles?". People are often completely puzzled by this question, so they'll accept that a notion may be useful even if it's not there to prove something.