What is the use of analog circuits today?
There are lots of examples that people will use that point out the "exception" to the rule where you can't use digital design approaches for signals, like:


dealing with RF or very high frequency signals, most digital motherboards in computers have a very "analog" design cycle.
conversion from the analog domain to digital.
Real world effects like stray capacitance, inductance and protection against ESD etc.
and many others and they are right !


They are cases where the rules used for digital abstraction breakdown.  In reality, there isn't such a thing as a digital circuit, it's just that it gets "packaged" to simplify the next level up of design.  And in higher performance designs reality arises and this packaging breaks down.

But we need not even look at these exceptions to understand that "digital" is a handy abstraction.  A very useful abstraction.

I'll take as an example the design of a simple digital circuit on the chip level.  One that is not particularly fast or even particularly challenging.  The designer goes in there and describes the design in say Verilog, sends the design off and gets the results back or loads it into a FPGA.  So we are not dealing with high speed mother boards, or RF and WiFi etc. that might "look" analog like.

What this digital designer is NOT seeing is the care and attention taken to develop and publish the parameters under which certain sub cells he uses in his design.  The cell designer, simulates the design of say a Dff under the PVT corners (Process, Voltage and Temperature) determines what level of error is necessary (3 sigma, 4 sigma etc.) and then comes up with the operating parameters under which the device operation can be considered to be "digital".  Then once fabricated they are tested against these simulations for verifications and corrections are made. For a Dff this would be setup and hold times.  As long as those timings are met under those conditions you can happily live with the assumptions that "hell analog isn't needed anymore".  But the next abstraction comes into play, synchronous design.  Now if we say that certain design regimes are followed, we can then design the individual cells in such a way you can cobble them together and not even violate those timing requirements above.  Unless you're doing something particularly clever or stupid.

Now once you have your slowish, "digital" circuit running, yes you can operate under the assumptions that it's digital and you won't get bitten.  But the reality is that everything is analog, the details are just hidden from you.  So the next time you use a "digital" uProcessor like a PIC or Arduino know that someone, somewhere has actually made your life easier by taking care of the analog aspect of nature so you can be deluded into thinking your design is digital.