What does melted butter do in a swiss roll recipe?
I have never added butter to sponge sheets when making swiss rolls, jelly rolls, or anything similar in the past. It's just straight up bread flour, sugar, and eggs.

I can only think of three possible reasons why butter might be added:


To improve the flavour;
To keep the sheets moist and help prevent overbaking, as any fat would be used in cake batter; however, this is generally not a major concern in cake rolls; or
To help prevent it from sticking to the sheet (don't bother; if you have this problem, use a silicone mat).


Reasons #2 and #3 aren't very convincing to me, so I would only bother adding butter if you prefer the taste of swiss rolls with butter added.

I don't think butter would help with rolling at all, in fact it might make rolling more difficult on account of making the sheets more crumbly and less able to hold together under pressure.