Yes, admittedly, you'd still have to transfer from the Beanstalk (which, like a very tall tower, is effectively motionless relative to the Earth's surface) to the untethered space station whizzing by (at about 8 km per sec) in low Earth orbit.
People currently "tend" (a curious choice of words on your part) to go to LEO not because there's anything intrinsically interesting there, but rather only because it's the nearest/lowest/cheapest "spot" which is nonetheless already in "true" space.
I, personally, have no problem with a long, stately "drive" into geostationary orbit. Who's in a hurry?
Regards,
The point of the space elevator is to launch payloads to interplanetary space rather than to earth orbit, although it would suffice for geostationary orbits.