It is cultural, but not written SOP, in my airline for the PM to read out wind components from the FMC - when relevant, or when requested by the PF.
Examples of when relevant could be:
- near performance limits
- near airframe limits
- changing rapidly
- expected to change rapidly
Is there a scripted mandatory go-around based on FMC wind only? No.
However, if I bent an aircraft and the FMC wind was outside limits approaching the flare, I would be seeking a good lawyer.