As they point out, we have Internet Archives, but that's just a copy and, while better than nothing, doesn't always preserve the original. I've got several different thoughts in my head after listening to Doc.
First, I think preserving things is worthwhile. When Doug Kaye decided to shut down IT Conversations, he did so early enough that he could "endow" its preservation at Internet Archives and pay for the preservation of the domain name, at least for a while. Consequently all the links still work. And the shows are still available. It's not perfect (e.g. the pictures don't load—at least not today), but it is preserved.
My second thought is that the Web is a fluid place. Hence the WayBack Machine. Doc and Dave are discussing blogs, and they grow but old stuff doesn't often change. (Hey! They're like blockchains! :) ) I can easily envision archiving and preserving blogs. Other sites are harder. I think about iMall, for example. iMall was an ecommerce company I founded with Ross Jardine in 1994 and worked on until we sold it to Excite@Home in 1999. There were thousands of variations to iMall.com over the years. The WayBack Machine has many of them, but not likely all. What does it mean to preserve that? I'm not sure. Maybe the WayBack Machine is the best we can do.
P.S. This new podcast needs an RSS feed!