There are engineers doing circuits the analog way, because they absolutely want to, or because they are forced to, or somewhere in-between; judging how much analog makes sense means stepping back and making objective assessments
I meet and speak with many engineers doing some analog design as part of their project, and they fall various categories, with some blurring of the boundaries. Starting at one side of the spectrum and swinging across to the other, I see:
The software engineer who has to do a little bit of analog (or a power-supply); he or she is usually not a happy camper
The novice, who doesn’t know why all this analog is needed, since everything "out there" is digital these days and, anyway, the project is mostly digital circuitry, processors, and code
The engineer who acknowledges that the unavoidable laws of physics dictate that certain functions, requirements, and constraints–such as line drivers, digital I/O, signal integrity, sensors and transducer interfacing, noise/EMI/RF–mandate "analog" thinking whether they like it or not.
The engineer who knows some functions are better done using analog circuitry and some are better executed in digital form, as a function of performance, accuracy, speed, power, cost, and many other parameters and priorities–and chooses accordingly
And finally, the die-hard analog designer who will never implement a function digitally if it can be done by an analog circuit; and who will never accept digital closed-loop control of a power supply; if it were even remotely practical to use analog circuitry for everything, he or she would.
What kind of designer are you? Are you too blinded by a bias–either from lack of experience or too much experience–that you can't look at the different ways of accomplishing the project goals, and matching them with respect to the project's priorities? That's what real engineering is all about. ?
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.