My guess would be that your approach would go faster, assuming that the cold water around the focused area doesn't suck the heat out too quickly, but perhaps not fast enough to be of practical use. Also, the maximum temperature that you could get would be 100 deg C; after that the water evaporates.

I suspect they use the graphite because the graphite can get much hotter than 100 deg with a simple lens. Coupled with its ability to wick up water into it, you could evaporate a substantial amount of water quickly.