They do exist today. We call them Rand Paul, Ted Cruz, Mike Lee and their allies in the Tea Party.
Get used to maps like this then:
You underestimate the ability of the Tea Party to make wise running mate picks. If Reagan (the Tea Party candidate of his day) could do it then who's to say Mike Lee wouldn't.
And you vastly overestimate the ability of a running mate to do more than "not hurt" a ticket. To use your example, GHW Bush's selection as running mate had negligible effect on the final 1980 vote.
Oh, and Dewey defeats Dole.