What's the best way to pull yourself directly vertical along a cable for 22,000 miles?
What's the best way to descend 22,000 miles quickly, but also with a braking mechanism that isn't going to require a heat shield?
Some sort of slow cable car going at 10mph even is going to take 2200 hours... 1000mph is going to take 22 hours still. That's a full day to orbit even going REALLY fast. And getting up to 1000mph vertically, for a sustained 22 hours... that's not an easy feat.
And if the goal is just to get up past the karman line and use the elevator as a stage 1 for a rocket launch and detaching from the elevator while suborbital is fine, then it's a one way trip, and still need to re-enter the old fashion way.
The scale of space makes all of the problems far more complicated (edit: not just the cable strength issue, but traversing the cable)