枯れる。涸れる。 (kareru)

In the intro to 「時代」/Jidai, Nakajima sings 「なみだもかれはてて」—namida mo kare hatete, tears completely (dried up). Everywhere I've seen this in lyrics, even in televised versions, the kanji used for かれる has been 枯, and I'm wondering why it's not 涸. Both kanji contain furui (old), but—ccording to EDICT/JMdict (via Kotoba and Denshi Jisho), at least—枯れる is more on the side of withering plants, and 涸れる is about drying up. This is even suggested by the hen radicals, 木 (tree) and 三水 (water droplets). Denshi Jisho lists many compounds with 枯 as blight, withering, or waste, many specific to plants. 涸れる compounds are mainly about lakes and water, drying up or running out. For tears, isn't 涸 the more logical choice?