Yes Mallory and others saw it a lot as they came in from that side (walked from Darjeeling!), and in later years climbed many of the peaks in that area NE of Everest itself (Kharta Kangri etc).
The Americans, led by Andy Harvard, actually went there in 1981, but failed, so went back (sans Harvard) in '83. I think Ed Hillary also went in on the '81 trip, just to BC, but got AMS. John Roskelley was also on one of these trips but left as he felt it was too dangerous and did not want to use O2.
The '83 team eventually used a rocket to fire a line up the buttress to mechanically haul loads. That buttress, now known as the Lowe Buttress, as George Lowe led most of it, looks terrible to climb. And those upper snow slopes just look like a huge crap shoot. Not surprising it's unrepeated. Lou Reichardt's summit meant that he is the only(?) person to have summited via new routes on both Everest and K2.
All this is just off the top of my head, too tired to reach for the library
The 2005 attempt might have been Cathy O'Dowd and her partner, but they never made much impression on the face, trying a line on the right hand side, underneath the Fantasy Ridge, I think. I believe the Koreans were trying the 1988 route, around 1999 or so.
The Chilean ascent in '92 was funny as it comprised some of the country's best climbers, but another lone Chilean was part of an international group on the normal S Col route at the same time. They ended up going for the summit the same day and the Kangshung guys were going crazy trying to get in front, so that the first Chilean ascent of Everest would be by them, by the better route. They didn't think much of the other guy
And I think they did just manage to get one of their guys ahead, and he was shouting abuse at the normal-route-guy on the last section to the summit!
I was wrong before about four ascents - it's three, as the Indians I was thinking of did not summit, they got to around 7000m on the 1988 route.
Should also mention that on the '94 attempt Steve Swenson was also on the team, and after they bailed, he went around to the now-normal North Ridge route, joined up with Eric Simonson's team, and summited without O2, becoming one of the few people to have summited both Everest and K2 from their northern routes without O2.
Another trip most don't know about is that months after the 1988 ascent, another team including a young Ed Viesturs tried a separate line but failed really low down.
Seems teams either summit, or get nowhere ...