Did Top Gear/Grand Tour Inspire a Generation of Overlanders?

It wasn't a recreational activity as much as it was just normal everyday life for travelers. "Overlanding" is a recreational activity, at least by today's expectation.
I'd have to disagree. Back in the early 1900s, nearly everyone who traveled just to get to a different destination would take a train. Sure, there may have been some who would camp on the side of the road while traveling without it being the point. But, millions of people back then specifically went on trips to stay in tents, cook outdoors, and experience nature as a vacation.

This article does a good job of explaining how it came to be.
How America Joined Its Two Great Loves, Cars and the Outdoors - Atlas Obscura
 
I guess people want the nostalgia of the past without giving up the technology and comforts of the present?

You mean like they did back in the past?
First paragraph from the article above:
"One summer weekend in 1921, President Warren G. Harding went car camping. He rode out to western Maryland, where a fleet of cars awaited: under a soaring white tent, the president dined in the wilderness with Henry Ford, Thomas Edison, and the other “Vagabonds,” who had spent every summer since 1914 exploring the country in a caravan of cars. Each year, their set-up grew more elaborate: in 1919, their camping trip required 50 cars, including one specially built to keep their food refrigerated."