AVRs are simple and reliable. You can read the whole datasheet and understand everything with much less effort than modern ARM MCUs. They've been around long enough that I have a lot of confidence in them. They're electrically more robust than most modern chips so they're hard to accidentally damage. There's a lot of community support available because of the popularity of Arduinos. Many tasks don't need anything more powerful. I think it would be foolish to discard AVRs as obsolete just because they're old.

AVRs are far from outdated. The AtXmega series is very powerful. It includes modern features such as DMA transfers. AVR chips are much easier to work with than ARM for certain applications. They are also lower power and cheaper. The OPs application would be significantly easier to implement on an AVR. On the RPi you would have to write a Linux kernel driver and deal with real-time issues. In the AVR you would create a few interrupt handlers and be done.

horses for courses. If you want a small microcontroller that has a very simple IO model then avr is great, and if you use something like an attiny they're cheap as ... chips.