Except for the fact that I favor Atmel AVR microcontrollers over PIC, none of what you are describing sounds all that strange even for new designs. There are a number of fairly old parts out there that have stuck around because they are well-suited to certain tasks; it would be a waste of time and money to reinvent the wheel. New parts tend to be fast parts. Fast parts can actually cause serious problems in situations where speed is unnecessary, such as in a keyboard embedded control system, for example. New parts also tend to carry a price premium that cannot be justified in commoditized products.
Also, I am 25 years old, yet I favor assembly over C for most of my simpler microcontroller projects because I can get the job done faster and I have more control over the hardware that way - so it isn't just something "old" guys use. Granted, I wouldn't be using assembly for anything really huge and complicated...
It isn't always what the parts are so much as what you're making out of them. It sounds like making keyboards does not excite you much. I can't blame you, really. But remember that you can do some amazing things with a pile of 20 year old op-amps or a fistful of 74HC chips. I would find another employer that will let you explore more interesting directions.
As for the advice, I'm not sure what you mean by an EE job that does not involve any "actual design". Even if you are not designing products, but are working in some sort of R&D or testing or failure analysis or troubleshooting role, you will still need to employ the same skills you would exercise as a designer. If you are asking if there are any EE jobs available which do not involve any thinking, well yes, there are two: management and assembly line worker. However, I suspect some common sense and thinking will still be required as an assembly line worker.