I can't remember where I saw this, it was either a fan game or a fan fic or a comic or something, but definitely non-canon explanation of Frog's Shakespearean speech that I really liked.
What if it's easier for him to speak in the archaic dialect? His mouth (among other things) was severely warped during the transformation, and pronunciation of the English (or any human) language requires a specific setup, so to speak. Perhaps the more formal pattern displayed more positive results as far as other people being able to understand him.
And if not, maybe that's what Woosley was thinking.
Anyhow, I remember when I was like 8-9 and thought it was cool then, kind of made him feel more like a Middle Ages knight. My friend Joe (with whom I played a bunch of RPGs "back in the day") and I would voice-act while playing, and doing Frog's voice was the most fun of all! If not for Woosley, things would have been very different. That's for sure.