These are not addressed in pop-sci articles, but are actually considered quite seriously. There is lateral force from the climber to the cable, yes. But if the

These are not addressed in pop-sci articles, but are actually considered quite seriously. There is lateral force from the climber to the cable, yes. But if the net mass flow to/from the top is zero, you don't have to compensate. You only compensate for the net flow. You do that by applying orbital corrections to the station at the top. If the climber is not rising at hypersonic speeds, the lateral force is pretty tiny - literally lost in the error margin, compared to the tension in most of the cable length. The climbers would have to rise fast, and the journey would be long anyway, yes. Basically, we would have to marry high-speed train technology (for speed) with Orient Express or ocean liner amenities (against boredom). The view would be spectacular, and would be a major part of the entertainment. It's probably best to build cables in pairs, one going up, the other down.