To push it out in to space like Voyager requires a lot of thrust, so I bet that's the reason.
As far as I can find, it's kept in the L2 point mainly for temperature reasons.
Not an expert, but this is what I gathered from https://space.stackexchange.com/q/23238/13952 and https://space.stackexchange.com/q/38408/13952
From what I can tell I don't think that it's very uncommon that these things are designed for 5-10 year missions and that everything else is just a nice bonus. I don't think anyone expected Hubble to survive as long as it did for example, and even the Voyager program was originally designed to be finished in the 80s and I don't think anyone expected it would last this long either.