Let me see if I can stick myself in the middle of the "DSP on ARM" sub-discussion here.
First of all, an ARM is NOT a Digital Signal Processor. Some ARM cores have Digital Signal Processing-friendly instructions, but they are not what I would call a digital signal processor.
Years ago, if you were doing signal processing of any meaningful sort, you really wanted a Digital Signal Processor. General purpose processors didn't really have the steam. Heck, I remember when you couldn't even reliably decode a MP3 on a PC. Any time you wanted to do signal processing work you really needed a processor which was optimized for that.
Time has gone on, and the applications that required a DSP 30 years ago can be done in a general purpose processor today in real time. And many of the processor cores have added DSP instructions to make it easier. If you're processing audio, generally you're going to be able to do that on a fast general purpose processor. That doesn't mean that a general purpose processor with DSP instructions is a Digital signal processor, it just means that the applications where a real digital signal processor is needed have evolved. And many of these applications have moved from a processor to a FPGA.
In a university class on "DSP" I think there are two main things which should/could be covered (I said some of this in a previous reply):
1) Digital signal processing algorithms, (filters, transforms, etc). This doesn't need a digital signal processor - instead can be taught on pretty much any processor. And for many applications, a general purpose processor would be the ideal end-product processor.
2) Digital signal processor architectures and how they are useful and how they differ from a general purpose processors. *IF* you want hands-on work in relation to this topic, then you need to find a processor which is simple enough to comprehend that you could actually be able to utilize it in the limited time given during a course.
There are still lots of applications out there where a real DSP is the ideal choice. There are some $1-2 real DSP cores which can do incredible things at very low power (motor control (aka BLDC), power supplies). There are also some very high end DSP's (and FPGA's) which can do signal processing that we only dreamed about just a few years ago. And yes, there are the general purpose cores which can handle far more applications than they did in the past.
I just think that making an argument that "you don't need a DSP to do signal processing" is just as bad as making the argument that "you need a DSP to do signal processing". The key is to understand the underlying algorithms of signal processing, and then understanding the tradeoffs between a real DSP core and a general purpose one. Sometimes the correct answer for a given product is a cheap general purpose core, sometimes the answer is a real DSP core, and sometimes the answer is a FPGA. Or a mixture of the above.