Every community decides on their own how they'd like to be gender neutral. What works for German may not work for Spanish, what works for Spanish may not work for German. My point is that "you can make that case for Spanish" is irrelevant for German, and vice versa. "Ärzt_in" is what the German speaking community is tending towards finding acceptable.

Re neuter making a difference (imo): it's because then not only are you trying to include enbies, you're very consciously trying to avoid making enbies neuter, as that's typically associated with inanimate objects. It's "der Arzt", "die Ärztin", but you probably don't want it to be "das Arzt[nb-suffix]". So you start playing around with gaps, male-female combos, etc. What's the determiner situation in Spanish? Maybe I'm wrong and you have the same problem.