I thought they found part of the plane they were in several years ago. It was on or near one of unnamed islands that is basically little more than a sand bar

I think that in both cases, we can apply Occam's razor and assume that the explanation which requires least speculation is likely to be correct. Earhart, as Dahermit says, wasn't an especially good pilot (albeit a brave one) and took a rather cavalier attitude toward navigation, so it seems probable that she crashed somewhere en route to Howland Island in the Pacific. Amundsen's aircraft, meanwhile, crashed in the sea off the coast of North Norway. We saw in 2014 when Malaysia Airlines Flight 370 vanished that even today, with dedicated search and rescue missions equipped with the latest technology, it's sometimes impossible to locate missing aircraft when they crash at sea; in the 1920s and 30s the search mission would have been far more rudimentary, and the longer someone is missing the less likely it is that they'll be found - aircraft in those days were rather spindly and would not last long in the water, nor will a corpse.

Of course, one day some traces may be unearthed - there are still plenty of people looking.

It is not likely that the Amelia Earhart mystery will ever be solved. Time diminishes the available evidence. The truth is that she was not, despite her popularity, anything more than a mediocre pilot who would not always accept the navigation instructions from her very skilled navigator, Fred Noonan. It is also notable that she neglected to prepare properly for her flight, refusing to learn Morse Code resulting in her using the more short-ranged voice radio and even then not using correct voice procedure such as counting into the microphone instead of whistling to allow triangulation of her position.

It's a big world out there... They will be found in a few hundred years...