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I have not looked Idle issues in the last few days because I am working on the unmaintained (since 2006 and 8), embarrassing (~5 bugs in 70 lines), disfunctional mess that tokenize.untokenize has been. It will take me a few more days to finish.
Clearing the shell window strikes me as an obvious beginner feature. From what I have read here, Squeezer strikes me as the sort of advanced feature that you and others have suggested should not be added. I might change my mind after trying it out. I must admit that switching from a half gigabyte 32-bit xp machine to a multi-gigabyte 64-bit win7 machine a couple of years ago seems to have eliminated large output slowdown. Or maybe tk has improved. Either way, not having the problem Squeezer solves probably colors my thinking.
So *at the moment* I would be inclined to apply a more or less Squeezer-ignorant patch like ClearWindow-extension and then revise Squeezer to replace methods as necessary when it is installed.