But wouldn't it be an interesting twist if old Dumbledore knew about the plans and his begging in the end was a last insistance for Snape to kill him? If you want to look at the grand scheme of things here, Snape didn't kill anyone except Dumbledore. He had Flitwick, Granger and Ginny under his thumb- and including his extreme dislike of Granger and anything Weasley- how could he have not done *anything* when he had the option?
His cover was going to be blown anyway, right? What difference did it make if he took out a blood traitor and Mudblood? It doesn't make sense.
Not to mention, both Dumbledore and Snape are skilled wizards in ligilimens. What's to say Dumbledore didn't tell him to do it in his last few moments? He was fully able, even weak and without a wand. And even in the face of death, do you really think Dumbledore would *beg*?