I think you describe job specifics about being an engineer accurately. Setting aside trying to differentiate developers and engineers, I like to say a "good" engineer is replaceable. Meaning, if an engineer has done a good job, another "good" engineer can come in and take over. This concept doesn't really describe what an engineer does, but it creates a pseudo-litmus test for how to approach a problem.
In traditional engineering, like mechanical or chemical, change in the field happens slowly. Standardizing tasks has happened just because time has allowed for it. I think professional software development/engineering/whatever you call it is trending this way.
Example: I studied chemical engineering where we learned how to size a tank that would be pressurized containing some hydro-carbon. You pressurize it to keep as much of it liquid to minimize the tank size; now you have to figure out how thick the walls of the tank need to be to handle the desired pressure based on the expected liquid composition and volume, among other things.
Are you surprised if I say this was stuff chemical engineering programs cover in the last year of study? In the previous 3 years, topics include thermodynamics, physical/organic chemistry and other much more analytical, bookish things that outsiders consider chemical engineering to be about. In oil refining, where all the money is as an undergrad, they're paying you to size a tank.
If you consider the historical timeline of when these topics could be considered "understood", the way the course plan is laid out might make more sense. To roughly break it out, we understood a lot more about lab scale chemistry pre-20th century than we did about tank sizing. Tank sizing is really heuristic and fudge-factor driven. IIRC from our textbooks, a lot of these were lab determined in the 1930's and 40's. They basically built a tank with some thickness and size, then drew up a list of liquid compositions with different properties and starting measuring pressures. The plotted data would get curve fit and, viola, a formula for how to size a tank.
You can't use the formula without understand your liquid compositions, which doesn't really work if you don't understand thermodynamics and physical chemistry, but it is also really hard to use only thermodynamics and physical chemistry to figure out how to size a tank.
So if I were to say where software is today, it's that we haven't standardized how to size the metaphorical tank, where that tank could be, e.g. different data access permissions for hospital records?