Can you expand on how analog electronics benefits in particular from a formal EE education? I build analog circuits (amplifiers, filters, power supplies mostly) very frequently in my job as a physicist. We have to care about noise so I've picked up a knowledge of how to deal with it in analog circuits. Is there some other area of analog electronics that "hackers" like me might not get exposed to, compared to an EE undergrad? I'm thinking of moving into EE and would like to work out the gaps in my knowledge. I also ask because I can see obvious reasons why your other example - RF electronics - would benefit from formal training but none for analog electronics.
More advanced stuff that you probably lack vs a practicing EE or an EE graduate education is going to be edge cases, advanced stability analysis, translinear logic and exposure to all the different types of component design. There are tons of different types of say amplifiers used in specific applications whereas most people working in a lab just slap opAmps on everything. A lot of advanced analog design is just applied control theory. Also keep in mind that these days Digital, RF, and Analog all blur a lot in a cutting edge design environment.
Quick Edit: A lot of the more traditional EE design companies will consider someone with a physics degree to be equivalent to someone with an EE degree unless they are looking for a very specific niche.
But if you can design an amplifier or power supply, you probably already understand how to think of all the basic circuit elements and write down a differential equation modeling the circuit behavior.
With respect to RF, it's also a large field. In lower frequency regimes you can model everything as a lumped circuit element. As you get into higher microwave frequencies, you start needing to worry about modeling things as a distributed circuit. If you are focusing on things like antennas then you need to know more about electromagnetics. These days practicing engineers dealing with things like antennas and feedlines typically model them with computers. In some ways RF analog circuitry is disappearing as ADCs and associated digital circuitry are becoming advanced enough to swallow large bandwidth signals.
In many ways EE is pretty close to "applied physics", just focusing more on emag and less on mechanics.
EE is a vast field that encompasses everything from high power transmission to designing semiconductors. Even full course work from undergrad to PhD in EE is going to be fairly specialized.
All that being said, I agree that if you just want to learn how to build a catalog of reasonably simple circuits, learning academic EE is a waste of time.