I hope I don't get a wise answer like, "If the kit comes with them, they're important." That may be. The reason I'm asking is because I know of a few people that have removed them from their Piper Cubs, with no ill effects.

Is is the long, slender wing of the cub (and Citabria, etc) that make the struts important to structural integrity?

I have a cub with a 76" WS, and I fiberglassed taped around the entire wing joint. The wing gets securely bolted down to the fuse.
How is this plane any different than any other plane, with just bolts, and no wing struts (or just rubberbands, for that matter?!)