As a cyclist, I can tell you that it's not about experiencing the challenge of climbing everest on a bike (and nobody who did it claims that). It is a challenge about gaining a very large number of vertical elevation on a single climb, which requires a combination of endurance, planning, practice and dedication.
Using the height of Mt. Everest is simply a good target because it is a very big challenge to climb 8848m and in addition combines this challenge with the most famous mountain on the planet. FWIW, there is also trenching, i.e. descending the depth of the Mariana Trench, ~11000m, on a single ride (which requires climbing the same amount; https://www.youtube.com/watch?v=dFQ5fVjQACc), and nobody claims that this is equivalent to diving down there.
and notably, if you actually climb mt everest, you start well above sea level so the total ascension is much less than 8848m. Clearly not a direct comparison
In case anyone wants the numbers, Everest base camp to the peak is 3485 vertical meters. But this is done over multiple days. From camp 4 to the peak is "just" 850 vertical meters, less than 1/10 of the 8848m Everesting climb.
Using the height of Mt. Everest is simply a good target because it is a very big challenge to climb 8848m and in addition combines this challenge with the most famous mountain on the planet. FWIW, there is also trenching, i.e. descending the depth of the Mariana Trench, ~11000m, on a single ride (which requires climbing the same amount; https://www.youtube.com/watch?v=dFQ5fVjQACc), and nobody claims that this is equivalent to diving down there.