I know some of you men are pure of heart, and that Heidi Klum could walk in front of you naked and your only thought would be to compliment her nail polish. I'm not talking to you, and neither is the verse in consideration.
I and the verse are talking to normal, single men, and the touching is not "petting," but touching. It's saying it's good (expedient) not to touch a woman. This isn't saying that helps, mercies, necessities and what proper decorum may require are not good.
It's saying that it's expedient for men to avoid touching women (they find attractive). Why? Because (normal) men can be enticed thereby. I remember a Ken Burns documentary on the Civil War. The Union army advertised for nurses to tend the wounded. The requirements? Over 60 years of age, or plain and unattractive. (I wonder what it would be like to live in a society where people aren't enslaved to political correctness or to the dishonest appraisal of the hearts of men.)
I also remember Elisabeth Elliot's recalling what Jim told her when, on one of her dates, they merely clasped hands. (A cursory Internet search did not reveal it.) Maybe someone here has read it? I think it's in Passion and Purity, but I don't recall exactly.
And, I recall the godly advice to teens who are dating, why it is good that they abstain from physical expressions of affection until their marriage is solemnized.
These things are good. I would not accuse those of sin who did otherwise (necessarily), but I couldn't commend them of doing well, and neither would Paul.