The zh in Tamizh

I've always wondered who came up with the idea of using the letters z and h to get the zh sound, which is exclusive to only tamil & malayalam. If that sound is not present in other languages, we should use something thats very close like the letter L. In fact, many tamilians pronounce tamizh as tamiL. So L would've been a better choice. Even Captain Vijaykanth says TamiL (right kaps?). South Indian languages dont have certain sounds that are present in N.Indian. But we make do with whats available and get the closest possible sound. But using z and h totally defies any logic. Any non-tamilian would say tamiz and not what we desire.
I tried something different recently. To make my American friend pronounce the word properly, I wrote T-A-M-I-R and lo behold, he pronounced it exactly the way it should be pronounced. Whoever came up with the 'zh' idea must be a creatively-challenged person. Don't you think so?