On GPUs, ML "just works" (inference and training) and are always order of magnitude faster than whatever CPU you have. TPUs work very well for some model architectures (old ones that they were optimized and designed for) and on some novel others can be actually slower than a CPU (because of gathers and similar) - this was my experience working on ML stuff as an ML Researcher at Google till 2022, maybe it got better but I doubt. Older TPUs were ok only for inference of those specific models and useless for training. And anything new I tried (fundamental part of research...) - the compiler would sonetimes just break with an internal error, most of the time just produce terrible and slow code, and bugs filed against it would stay open for years.
GPU is so much more than a matrix multiplier - it's a fully general, programmable processor. With excellent compilers, but most importantly - low level access that you don't need to rely on proprietary compiler engineers (like TPU ones) and anyone can develop something like Flash Attention. And as a side note: while a Transformer might be mostly matrix multiplication, many other models are not.