The US doesn't have a significant problem with deliberate acetaminophen overdose as part of a suicide attempt, which is the problem the UK rules are meant to address.
Strictly speaking, if you wanted to solve intentional overdoses of acetaminophen, it appears that you could do it by presenting more appealing means of self-harm, like in the US. I'm pretty certain the availability of other lethal products (guns, really) directly correlates with whether OTC drug overdosing is a popular means of harm.
I'm willing to bet that handing out cyanide pills OTC would effectively eliminate intentional acetaminophen poisonings in the UK. Surprised the boffins at the NHS didn't think of it first if they really want to eliminate intentional overdoses! /s
There's some research to suggest if you make suicide a time consuming process some percentage of people who decide to do themselves in will reconsider while they're trying to carry out the act. I'm skeptical, but I understand the reasoning.