Much of the real world indeed is analog, and needs to be treated as analog. Sometimes a digital approach makes a lot more sense, but I see way to many places where a digital system is used when a very simple analog circuit would be better, cheaper, simpler, and have a much shorter debug time. So there does exist a bias by those who fear analog, and unfortunately it drags us into the realm of software, compilers, processor memory speed and size issues, and that biggest of all concerns, de-bugging project delays. WHo can afford to spend an extra week or three debugging code in order to be able to try it and see if there are hardware problems. That is where analog comes out on top. On the other side, I don't think that an analog word processor would be practical. Which proves that there is a place for each.
I'm somewhere between 4 and 5. The engineering world is much bigger than a kitchen, where there is more art to it than engineering has. We need specialists ... would you have a G.P. do your brain surgery?
But I revile those Analog Engineers who discharge digital as not real and try to make a front-panel button responder out of a discrete transistor bistable, don't lets forget that the wave-particle duality is still a duality and at the foundation of Maxwell is some quantum stuff that I don't have time for (yet.) Magnetism doesn't exist ... it is a convenient handle to explain phenomenology of relativity of pure ElectroDynamics (no magneto-) There are no linear time-invariant systems bigger than epsilon in both space and time, our linear approximations are just that ... approximations.
Really, though, I love the trajectory of I vs. Vbe. I can't wait to hit f11 then [ins]. I get bored quickly with type casting, signals and exceptions thrown. It's a preference and not a chauvinism. A love and not a religion. I am an Analog Engineer ... Signal integrity, amplification, noise gain ... ahh the sounds of FUN. I'm SO glad that there are people who love digital and software design so that I can leave them a nice bit of fun too.
We need to find was of teaching engineers to be all-rounders. If there are places in 'design space' that you fear, you'll come unstuck one day.
There's a strong analogy with the restaurant kitchen. Some chefs are creative on the main course, while some are natural pastry chefs. The great chefs understand all the stages, and more importantly they can put a whole coherent menu together - they are the systems engineers of the dining world.
So, all you students out there (young and old!), make sure you take both the algorithms classes and the differential equations courses. More tools = more flexibility in understanding how to solve your problems.
The real world is analog, so even the most die-hard digital designer must occasionally wear an analog hat. But the most intriguing question you raise is that of optimizing the mixed-signal solution for "performance, accuracy, speed, power, cost" and don't forget schedule.
Analog and digital engineers not only tend to see the world in different ways, but they also use very different tools and methodologies to design, implement and verify their respective solutions. It is sometimes difficult for us to understand each other's perspective, even when working on the same project together!
Ultimately, good system engineers are needed that can speak both languages and can make those A vs. D trade-offs and optimizations, and ensure that the overall team delivers the best product in the right timeframe.