Yep, AVX is nice, but still it is far from current DSP chips.
I ported a subset of PHY to real AVX2 CPU and AVX512 sim. It is (sometimes) comparable to c6x (which is a crap DSP) if you take (much) higher clock into account, but comparing to current DSP IP cores it is a joke.
Regarding FPGA, of course you don't do the complete implementation in it, you accelerate the low level stuff, FFTs, coding, etc, as are already done in all baseband dsps.