When it comes to the signaling theory, I mostly agree. But I think there is a spectrum.
For example, someone with a degree in chemical engineering is obviously going to be much better equipped to enter that field than an equally bright person who did not study ChemEng. I think MDs would mostly be an exception from signaling theory, but I understand that that is totally different from an undergrad degree. I'm sure signaling plays a role in the more competitive specialities, but you get the idea.
On the polar opposite of the spectrum, an example would be an elite MBA (Harvard, Stanford, Chicago, Wharton). These degrees are almost pure signaling. Essentially, if you got into the program, you have the "mark of approval", and what you take away from the coursework is up to you. It doesn't matter, blue chip employers will be lining up to hire you regardless.
And then there's everything in-between. I'm mostly in agreement with your take on signaling, but I think there is some nuance to consider.