Why would I have to walk all the way to the top of Mount Everest? Couldn't I just fly?

I have been pondering this question for a day or so now, and can't really see why I could not just get a mate (Dave, or Robert - or maybe even Derya?) to fly up there and plonk me on the summit?

Mr W., when asked, said he thought flying wasn't an option because it would be "too high". I think; OK, how high is it? This says its peak is at 29,000 feet above sea level. Which seems high but not that high - I remember seeing numbers in excess of 30,000 feet (on the little information monitor on the back of the seat in front, relating to feet above sea level) when flying - but that might be only on commercial 'planes.

Mind you, that link does also say the peak is "a place where helicopters do not fly". Do helicopters have a lower maximum altitude? Or is it because helicopters are more unstable or something? Or is it likely that if helicopters don't go there, then 'planes don't either? And is it a case of "do not" or "can not" fly to the peak of Everest for both 'planes and helicopters?

If I found a pilot with a lot of experience in flying in mountains and ask him to give me a lift, could he do it? I mean: Could one fly in a 'plane to the top of mount Everest or not?

A bit of a google later, and I found this which makes it seem as though flying high isn't the only potential problem. Apparently the Chinese have some air space in the area and can refuse permission. However, this chap was in a balloon not a 'plane.

Interesting

*strokes chin*

So, I've given you some starters (things that I just found out but that most of you already knew, I'm betting). You've all got huge brains and skills in different areas to me (unless you count mediaeval history. in which case you've got the same skill set). Could I get to the top of mount Everest by 'plane and if not, why not?

Answers in the "comments" box please. Prize to the most interesting reason why I can or can't fly to the peak of Everest.

[Prize might have no actual value in this world and quite possibly the next]

**UPDATE**

Mr W. pointed out he might not have been being serious when he said mount Everest was too high when I told him I referred to his opinion in a blog entry. I thought I'd better mention that because he didn't know at the time (when he said it) that he would be quoted and it's slightly possible he didn't realise I take most of what he says as absolute gospel. Personally I would have thought that by now he would be aware that I tend to take things at face value. I mean, I'm still getting over the sun not being a dead star. Anyway, enough disclaimers.