Modern x86 is quite competent as DSP using AVX. I think you are exaggerating. I have worked with LTE baseband as well, but admittedly never done an x86 LTE PHY. pCell claims to be doing quite complex network mimo LTE stuff on x86, still mostly vaporware though.

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.