I can't agree more with your judgement. I've read all these three books and the fact is just like what you mentioned. CLRS and TAoCP use a lot of space to prove the algorithms correct(especially TAoCP, it even uses different ways to prove one algorithm) and that makes me feel dizzy. Perhaps I'm just a programmer not a computer scientist.

But I have to say that use some time to read CLRS and TAoCP is worthwhile. It will help u know more about algorithms and avoid the condition that just know how but not know why.