My guess is that the slogan derives from the Sean Bean Yorkshire Tea advertisement, which captures the county's self-image perfectly. Nothing like it would have worked for any other county in the country, but it's just how Yorkshire is. People in other counties found the ad amusing for poking fun at Yorkshire, but most Yorkshire people are really quite pleased with it.
If you ask people in England where they come from, most people will respond with the name of the town or city they live in, or say "near" a town or city. People from Yorkshire will respond with the county rather than the city, though. Only the people of one other county do that: Devon. I don't know if this is because Yorkshire and Devon are the two largest counties or not, but I was told this fact by a woman at an academic conference back in about 1982, who, upon hearing me answer "Yorkshire" to her question "Where are you from?" stated that she was from Devon and then pointed out our common quirk. Over the years, I've observed that in general it's empirically true, too.
"Do it for Devon" doesn't have quite the same resonance, though.