Accessibility and familiarity.
ARMs generally make poor DSPs, in relative terms -- they're general-purpose CPUs and MCUs -- but even the lowest level options are more than capable for a lot of simple applications like audio mixing and effects, or, Idunno, MP3 decoding? Not to mention vector controls like FOC, or, Idunno, some SDR maybe, even some light video processing or rendering (obligatory
itrunsdoom).
And, that said, you can get ARMs with a ton of extensions, whether in terms of instructions (FMAC, FP, SIMD, etc.), or hardware support (advanced DMA, say?).
I know a lot of TI and other relatively small or proprietary MCUs/ISAs require buying dev tools, haven't looked at that family specifically but needless to say it's a huge differentiator between hobby/amateur use (PCs, ARMs and Arduinos everywhere!) and professional use. And no one's talking about the latter, because it's all on internal forums, or served by internal support, and concerning confidential projects for companies/clients. So, confirmation bias too, but that also happens to feed back in marketing terms as ARMs for example are so popular, found in basically anything, has broad support from free tools, that aren't even awful (indeed GCC is supported by many manufacturers).
That last point, kinda just to say -- I mean, there are many reasons why and why not, some good, some bad -- but a basic review of avr-gcc (e.g. Arduino on any AVR platform) output shows it's pretty rough; whereas the optimization for ARM, x86, etc. is quite good (AFAIK). And this is a minor point, of course -- if you need sheer CPU cycles, you're simply barking up the wrong tree using AVR, anyway.
But, that said, AVR can be used to modest effect, perhaps with a bit of optimization effort (and fortunately AVR asm is rather easy, as ISAs go) -- I made a reverb effects box, mono 12 bit x 25kSps, using an XMEGA. That's just about rough enough to still be useful; any fewer bits, or a lower sample rate, and it would be probably too unpleasant to use. 16 bit x 44.1kHz stereo would of course be preferred -- that's not going to happen here, but would be easy on ARM.
Not that this is all that relevant, if you're talking TMS320s versus Cortex M4s.

Tim