22,000 miles would need a really big counterweight. Easier to make it longer instead (several times - I think about 60,000 is the accepted figure), and then you can also use the whippy end to launch deep space craft at dozens of miles per second.
And the idea for elevators is multiple cars. So nobody cares if it takes 24hours to reach the top.
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"I would rather be exposed to the inconveniences attending too much liberty, than those attending too small a degree of it." - Thomas Jefferson