if the environment within
vertical tunnel/elevator
can be controlled,
with electromagnetism
and control of speed,
there shouldn't be any effect
on contact with the atmosphere
(when it reaches that height)
you can move up slowly,
or just fast enough,
and the environment within
is probably free from any
friction/temperature effect...
the rocket need only to land itself
on top of the elevator accurately
when coming back,
and reintroduced into the tunnel
to descend down.
tunnel, could be pre-designed
to be.... accommodating these rockets.
whichever is more advantageous.