The answer to that question is quite tricky because the spirit of the law gets much less discussion in the literature compared to the letter.
A simple explanation is that God restricted Jews from 'work' that affects the world in certain ways on Shabbat in order that they should rest. For example, no building, or lighting fires. However, they can benefit from pre-existing fires or buildings.
Pressing the elevator button is akin to one of these forbidden effects (which one depends on a broad discussion about electricity on Shabbat), going against the injunction to rest. Walking in to the elevator and it moving automatically is more similar to benefitting from an existing fire.
While it may seem strange that pressing the elevator button is considered 'work', the answer to that is that the definition of work is directly related to the laws and not necessarily some external metric like effort. This means that the spirit and letter end up very closely related, but I think the distinction still exists.
For sure, the main reason for Shabbat elevators is for people who have trouble taking the stairs. My alternative approach still does hit every floor, just on every second pass allowing people who can take the stairs one floor to decrease their waiting time.
I wanted to post an alternative approach to 'rules lawyering' in Judaism in contrast to the 'loophole' approach taken by some comments in the thread:
God does not have a vendetta against elevators. God decreed specific sets of rules that make actions on the Sabbath forbidden, as interpreted by rabbis over the generations. When new situations arise the rules are applied to the new situation to see whether it is permitted or forbidden. Sometimes, like with elevators, the consensus is that the new situation is forbidden. In such a case, if there is good reason, the question becomes: "is there a way that we can tweak the situation so that it doesn't fall into the forbidden category?". For elevators, the answer is yes.
This still follows the spirit and letter of the law, because the spirit of the law really only applied to the reasons that made the elevator problematic in the first place and not to the whole concept of elevators.
I am an orthodox Jew who lives in an apartment building with a Sabbath elevator. I usually takes the stairs on the Sabbath, but use the elevator occasionally. While in it, I always contemplate other possible strategies the elevator could use to speed up the runtime.
All Sabbath elevators I've seen follow the route `1,2,3,...,N,1,2,...` which can take up to `2N - 1` steps (open/close cycles) in the worst case (you just miss the elevator on the ground floor and are going up to `N`).
What if they went `1,2,4,6,...,N,1,3,5,7,...,N`? Worst case is still `2N -1` but if you relax the goal to only care about getting within one floor of your target (go one away from your floor and take the stairs for the last flight) worst case drops to `N`. (Each step would take a little longer due to having to travel 2 flights, but most of the time is spent waiting for the doors anyways.)
Has anyone seen a Sabbath elevator that doesn't follow the standard route?
A simple explanation is that God restricted Jews from 'work' that affects the world in certain ways on Shabbat in order that they should rest. For example, no building, or lighting fires. However, they can benefit from pre-existing fires or buildings.
Pressing the elevator button is akin to one of these forbidden effects (which one depends on a broad discussion about electricity on Shabbat), going against the injunction to rest. Walking in to the elevator and it moving automatically is more similar to benefitting from an existing fire.
While it may seem strange that pressing the elevator button is considered 'work', the answer to that is that the definition of work is directly related to the laws and not necessarily some external metric like effort. This means that the spirit and letter end up very closely related, but I think the distinction still exists.