Humans are not Vulcan-style compartmentalizing creatures, and no rule can stop love (and lust, contrary to puritanical religious-derived beliefs, lust is also ok), etc 100% from emerging. Tons of very happy marriages and relationships started in professional settings.
You can ban sexual advances in professional contexts, and achieve substantial compliance, and we should, just like we've done for racist statements. (There are things that Nixon or LBJ said that even Trump won't say!) The opposite viewpoint serves men to the detriment of women. I've never met a woman who said to me "you know, I just wish I could date more guys from work." The truth is (especially in the age of Tinder), most women don't really have to try very hard to get a date. So there is little benefit to them from social rules that make it okay to solicit sexual relationships in professional settings.
In exchange for those sparse benefits, there's real burdens. You're right about the puritanism in one sense: in America, work isn't just something women do to keep themselves busy. Today, work is their livelihood. It determines whether they have healthcare, where they can live, what schools they can send their kids to. Men get to go through their professional lives focused on work. They make work friends and establish mentoring relationships, and they can simply assume that those relationships are about work. Women don't get to do that. That coworker you're friendly with because you share similar ideas about TDD? Oh, he's actually just being friendly because he wants to have sex with you. That meeting with an investor that might be able to introduce you to people you want to know to launch your startup? Oh, he thinks it's a date.
Some consider a hug sexual harassment, some consider touching a knee. What about putting your hand on a person's back? Does it make a difference what part of their back, if so exactly how and where?
Sexual harassment should be far more about intention rather than the specific part of the body touched (excluding the obvious no-go areas of genitals and breasts). Generally you should be allowed 1 strike, for mis-reading signals.
In a society where men are expected to initiate contact, this is a fraught situation.
It is not a simple answer.
Can you imagine the following scene:
"Gee John, you did a great job there, I would like to shake your hand, or even pat your back (only near the shoulder mind you and no lower than a line formed by the bottom of your shoulder blades). Do you think that would be permissible? I want to reassure you that this touch will not be sexual in any way."
As for patting backs, do avoid doing so. Many of us don't like it even if it's totally non-sexual.
...and many of us do like being patted on the back (non-condescending of course).
Perhaps in the future, we will all have to work in an environment where no touching of any sort is allowed, ever, but I can't help thinking that would be a step backwards.
The couples who found sex and/or love (and even marriage) in the workplace, would argue that it's appropriate.
It's only when it happens against the other's will that's inappropriate.
Merely some office decree saying it's not appropriate doesn't make it so (and if two people click, it won't fight human nature to connect, including in this way, anyway, people will do what they do).