Does anyone know why they can't simply send people up with all the modern technology like bottled oxygen to remove the bodies?
Now imagine that your rescuer, having successfully bettered Mr. Body's achievement by getting to his high point alive, now has to perform the strenuous physical labor of digging Mr. B. out of the solid packed ice, picking up his 200 pound corpse, and carrying it the entire way back down to base camp.
What odds would you give our rescuer of surviving that task? 100%? Perhaps somewhat less than 100%? Less than 50%, much of which depends on factors outside anybody's control?
Would you volunteer for that job?
As mentioned already, almost all climbers use bottled oxygen and have done so even in the first ever summit by Hillary et co. The climbs done without bottled oxygen are extremely rare and dangerous, only a handful of people, all experienced climbers, have done so. Bottled oxygen doesn't make you function as well as at sea level, it just prolongs the period a climber can spend in the death zone.
But climbing at that altitude is difficult and hard work all the time and there are some narrow ledges and vertical climbs where climbers will essentially have in a queue one at a time.
And there's only a few weeks per year when you can actually access the mountain summit. Most of the year the winds in the jet streams will blow at hundreds of miles an hour making the summit inaccessible. During the few weeks preceding the monsoon season, the jet streams will slow down and during that time there are so many climbers going up and down that it is literally crowded to the point that it is hard to move.
There have been a few successful rescue attempts of stricken but still alive climbers near the summit but the rescuers essentially risk their own lives to save their buddies.
An attempt to recover dead bodies at a risk to your own life is not deemed worth it, even if you disregard all the money and effort it takes.
Even with lots of aids, it's still hard enough just to climb the mountain yourself. Carrying a body down with you vastly increases the difficulty.
There's a substantial chance that anyone who goes up to remove a body will instead become a new body needing removal.
However, even if you deal with the breathing mix issue, you're trying to carry frozen bodies off a mountain while you've just encumbered yourself with a heavy cylinder and it's already difficult to move with all the clothing you need to wear to keep warm.
If you ever have to move a dead body around, you will find it is quite difficult even with 2 people to help manoeuvre the body. I seriously doubt you would do anything more than end up as another statistic - just like the Nepalese police inspector and Sherpa the article described who tried to retrieve Hannelore Schmatz.
In extreme environments, you do not always have the option for the civilized society niceties - they will kill you and, on Everest, leave you frozen to the spot.
Mount Everest & The Gas Laws [1]
[1] http://prezi.com/uyvudl1s2h7x/mount-everest-the-gas-laws/
Some of these were taken with zoom lenses. The guy with the white skin exposed on his back is not accessible at all, IIRC.