A key point with space elevators is that they aren't limited to Earth. The solar system has plenty of celestial bodies that could benefit (us) from having one.
It may not be as significant as the impact of an Earth-based one, but any propellant savings is a win.
A space elevator on Mars is probably totally feasible. But of course the benefits would be much larger on Earth.
The problem is: the benefit of a space elevator is bigger the deeper your gravity well is, but it's also much harder to impossible to make one there.
But I've also been wondering: wouldn't it be possible to have a tapering space elevator? Reduce the weight by making the parts that have to carry less weight thinner?
Yes, it absolutely has to taper, with an exponential curve, to keep stress constant over the length of the cable. The taper ratio (in terms of cross-sectional area) for the best currently available engineering materials for an Earth space elevator would be in the tens to hundreds of millions, but a carbon nanotube cable might only require a taper ratio of around ten. (A steel cable would need a taper ratio on the order of 10^33.)
It’s a function of area so if we scale equally in both dimensions, a taper ratio of 10 means a thickness ratio of ~3.2. But yeah, that doesn’t exactly buy us much.
It may not be as significant as the impact of an Earth-based one, but any propellant savings is a win.