Not only would profits be lower (disincentive for companies), Chinese [or other off-shore] employment prospects would be worse (disincentive for them to comply).
Trade makes people better off in general, but it doesn't make every person better off.
If China would make themselves less competitive "by enforcing equivalent, high working standards across the world", they have clear disincentives to enforce compliance.
Oh, yes. That's been used to drive down the standard of living in the US (including within it) forever. That's why competition is bad for labor. The only real escape from the market's race to the bottom is a democratically planned economy IMO.
Trade makes people better off in general, but it doesn't make every person better off.