I will tell you that I do have an idea for if I have to take a day off, not putting in a fill-in host but rather a radio mockumentary where I, the host, fictiously use the show as a base to rise to world power- only to lose it all- and we close with myself shouting about sports to people on the street.
I thought it would be good (and shameless) self-promotion and something that people would talk about for years afterwards.
But other than that, I think you're better off with live shows.
Side note- I will say that for special occassions, sometimes repeating a classic broadcast is not just okay- but fantastic. For instance, I know on Christmas a few years ago one of our local sports stations repeated the broadcasts of the Penguins winning the Stanley Cup and such- and it was great! Another station reran classic interviews of Myron Cope interviewing Art Rooney Sr. after the Steelers won the Super Bowl in 2008-09.
But yeah, rerunning a two-week old interview if your host calls in sick- lame.