Why not just do proper PID control in software? ...
Is there any real reason?
Yes, the reason is that it is way too easy to solve the problem with two resistors. There are countless analog power supplies, which have everything built it, and I can design a new power supply in an hour if I really want. With a microcontroller, you need an external switching device, usually a driver for it, voltage sensing for the feedback, programming port for your micro. Also, you need to take care, so a breakpoint doesnt blow up your carefully designed power supply, or it doesnt blow up the first time you power it.
And then you also need an extra power supply, just for the microcontroller.
Besides, digital control is slower than analog. And you can make a decent PID with 3 resistors, capacitors and an opamp basically.
And after you designed it, you need to characterize your supply, which is already done if you use an off the shelf IC.