analog computers don't generally compute by operating on symbols. For example see the classic video on fire control computers https://youtu.be/s1i-dnAH9Y4?t=496
OP's specific phrasing is that they "map symbols to symbols". Analog computers don't do that. Some can, but that's not their definition.
Turing machines et al. are a model of computation in mathematics. Humans do math by operating on symbols, so that's why that model operates on symbols. It's not an inherent part of the definition.
No, analog computers truly are symbolic. The simplest analog computer - the abacus - is obviously symbolic, and thus is also true for WW2 gun fire control computers, ball-and-shaft integrators, etc. They do not use inscriptions which is maybe where you're getting confused. But the turning of a differential gear to perform an addition is a symbolic operation: we are no more interested in the mechanics of the gear than we are the calligraphy of a written computation or the construction of an abacus bead, we are interested in the physical quantity that gear is symbolically representing.
Your comment is only true if you take an excessively reductive view of "symbol."
You keep referring to what we are interested in, but that's not a relevant quantity here.
A symbol is a discrete sign that has some sort of symbol table (explicit or not) describing the mapping of the sign to the intended interpretation. An analog computer often directly solves the physical problem (e.g. an ODE) by building a device whose behavior is governed by that ODE. That is, it solves the ODE by just applying the laws of physics directly to the world.
If your claim is that analog computers are symbolic but the same physical process is not merely because we are "interested in" the result then I don't agree. And you'd also be committed to saying proteins are symbolic if we build an analog computer that runs on DNA and proteins. In which case it seems like they become always symbolic if we're always interested in life as computation.