The semiconductor business in general has brutal boom/bust cycles due primarily to the large investments required to increase capacity. The cycles have somewhat smoothed out in the last 10 - 12 years or so (since the industry recovered from the epic dot bomb) but particularly in the 70s and 80s they were legendary.
I agree no one "NEEDS" a degree for anything. People can be mentored and learn anything on their own. One of the best intuitive analog designers I ever met, Jim Williams, didn't have a college degree. There is more to it than a bureaucrat driving a desk.
I'll tell you two reasons why analog IC design companies like to hire Ph.D.s. First, it's because they can hit the ground running and cost less to train. Advanced analog development is difficult and requires more expert knowledge than equivalent software or digital design because less knowledge is embedded in the tools and frameworks used in development. This is primarily because an analog design has more degrees of freedom than a digital design and can't be endless tweaked and updated like an Agile software development.
Now, to become a useful analog designer you really need to go through a full design cycle. You need to design a circuit in schematic, do the layout, do all the verification, tape it out, bring it up in the lab and characterize it, and write or contribute to the datasheet. If you hire a fresh BS student, he or she might have a bit of background, but you're going to have to hold their hand through this entire process and it could take over a year.
On the other hand, if you hire a Ph.D or an MS (from select universities), they've gone through this process in school and actually going through the process and experiencing it is where the real learning takes place.
So it comes down to companies wanting to hire someone to help RIGHT NOW and not being interested in training and developing their workforce. This is just another consequence of that general trend.
The second reason is the level of sophistication required from analog chips and macros is going through the roof as more and more of the system architecture is subsumed into the chips that comprise the system. I work on systems that contain analog adaptive equalizers (for serial links) and self-calibrated ADCs. Designing these systems requires a great deal of math and I would have a hard time understanding them if I didn't have a strong background in random signals, time series analysis, and discrete math. These are not typical things you learn as a BS EE focusing on circuits and 20 or 30 years ago analog ICs were more components of systems and now they are systems unto themselves.