I used analog PID controllers for years. Our company designed our own controllers and shipped thousands over the years. Around 1990 we made the switch to digital and never looked back. True it can take some cpu power to do it right, but the options available combined with no drift and perfect repeatability are big advantages.
There is a lot of good analog building blocks out today. Biggest issue is part stability over time, parts matching and thermal effects. Many of our analog controllers are still out there on a lot of machinery. A solid analog controller can still outperform a digital one in certain cases. Plus you rarely have "bugs" to worry about. On the other side, more complex controllers require more complex circuitry and more pots to adjust.
Paul