A couple of minutes delay almost never causes a missed connection in the UK, because connection times that the route planning service uses are more generous than that. You'd have to be quite unlucky: probably a combination of a connection from one end of the station to another and a mobility issue. Connection times are built around this scenario, but I don't think they build in slack for it.

I get travel anxiety but have never had my day "ruined" by a couple of minutes delay. It sounds like you might mean that the metric isn't useful for the very narrow scenario of someone who will get crippling anxiety from that, which is fair enough, but that doesn't make it "unrealistic".