I don't think Charles is very often right about things. Actually one thing Charles and Diana both agreed on was the boys schooling and in Harry's case I think they both got it wrong. They both wanted the boys to avoid the heartaches that Charles had experience in the rough and tumble school Gordonstoun and avoided sending the boys to anywhere like that at all costs. What they failed to realize that a very physical but less intellectually gifted boy like Harry would likely thrive in an atmosphere like Gordonstoun much better than where he did end up and where his cousins Peter and Zara actually did end up and enjoy it immensely. For Harry I think Eton was a big mistake.
I agree Eton was a mistake for Harry academically but I don't think that was Charles first consideration. I think the main reasons Harry went to Eton was that Diana died and I don't think the princes wanted to be separated. IIRC I think they were talking about putting him at Rugby although Gordonstoun probably would have been perfect for him. IMO if Diana hadn't died, Harry would have gone to school elsewhere.