That microcontroller costs a small fraction of the precision ground crystal it is boxed in with.
You need a way to calibrate the device after the package is sealed, that implies some smarts or you're going to end up with a whole raft of extra pins and that would be costlier than the microcontroller!
I'm sure there are alternative ways but in this day and age cpus and small amounts of flash + memory are priced a little bit above the sand they're made of. I have whole units packaged and with far larger capabilities for $3 Q1, and that's with a whole lot of assembly and other costly detailing.
Microchip, one particular embedded controller manufacturer lists their SMD packaged PIC16F15213-I/SN which is much more powerful than what you need here for $0.33, Q100 that drops to $ 0,27400. This is a complete device, not an unpackaged die, which would retail for a small fraction of that.
Control loops and analog stuff works well, but not if you also want to be able to do calibration after the fact package is sealed, I'm not aware of any tech that would be fully analog but that would have the same flexibility and long term stability, never mind mechanical stability (microphony, talking to a crystal is probably the cheapest and easiest way to get FM modulation!). Note that this is different precision wise from a device that simply measures the temperature and does a compensation based on that, the device you are looking at in this article is easily an order of magnitude better.
just because it is digital doesn't mean it has to be a microcontroller though, right?? i see no reason this wouldnt just be a state machine or whatever out of plain old logic.