I doubt that I'll have rich tooling and libraries to draw from when I need them.
If I build a game in C#, for instance, I have editors that can lint my code, perform intellisense, automate test generation, and a rich set of libraries I can draw from. If I don't want to write my own Hierarchical Task Network planner, I can use FluidHTN. Likewise, I can pull out my code from my project and modularize it for other engines/games -- maybe I've got a great state machine implementation or something I want to share. GDScript limits my reach.
The knowledge is also not particularly useful outside of working with Godot. Picking up C# from working with Unity, for example, translates to other domains easily if I want to change careers.
I also can't write my backends and supporting services in GDScript. If I wanted to , I could make my entire codebase in C# for both front end and back end code, simplifying my tooling and knowledge needs.
I don't want to be too down on it. I'm sure there are ways that it would save time. My use cases are much more about setting a high bar for ergonomics and engineering excellence for larger projects. I think that in my case, they've provided the Extensions and C# support route. (Though it sounds like getting those to work on all platforms is non-trivial today.)
I mean technically you can. Godot has a headless mode for servers, etc. I certainly wouldn't pick it as my first choice for all the other reasons you listed though.
In my case the main issue with GDScript is the tooling, or lack of thereof. No symbol aware rename, no go to definition/usages, poor autocomplete, cryptic errors. Also static typing that's kinda but not entirely there, which exacerbates the tooling issues.
Good tooling is an enormous undertaking, so the way I see it, GDScript is forever doomed to feel like someone's impressive hobby project.
e.g.: Using python, I can do games, scientific/bio work, math, web backends etc. The same time investment in GDScript will only net me experience with GDScript which right now only exists in Godot.
But suggest a different language or a DSL for something, no matter how much sense it makes (sometimes getting simple SQL in places is a political struggle, and it's unfortunate when teams develop a "regex expert" even though all the regexes are simple), even one that is already super similar to one they already know like GDScript and so is rather trivial to learn (no one's asking you to learn something on the order of complexity and different-to-others like Haskell here), and devs start putting their foot down and saying "Of all the things, I"m not learning that!"