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I suggest an easy to implement idea. Not anything new, and something Konqueror already supports : session restauration.
Actually, when you close Konqueror, you can't ask it to remember your session. You have to save it yourself. However, if you kill it, it will restore the session. I suggest the dialog asking the user if he wants to close the whole window or a single web page be used to ask him if he wants to save the session for the next time Konqueror is loaded.

This idea is technically a duplicate of hKonqueror sessions/view profile, but since that idea is invalid under current rules I am approving this idea.