Any fool can type a letter, also referred as a form letter. Sure , i have used these in the past. But, personally writing to a celebrity (not always in cursive) shows you honestly cared enough to spend the time on a letter. Plus, sometimes you will receive extra perks such a a reply letter, extra graphs, etc. Some of those harder to receive graphs respond more to hand wriiten letters versus typed. But, in the end it is your decision.
I don't think it matters whether typed or handwritten. Either way, you want to customize the letter to the person you are writing to, that's probably what matters.