In the episode, Provoost explains the benefits of burying a soft fork, in particular how it helps developers when they review the Bitcoin Core codebase or when they perform tests.
After explaining the benefits, van Wirdum and Provoost outline a potential edge case scenario where burying soft forks could, in a worst-case scenario, split the Bitcoin blockchain between upgraded and non-upgraded nodes. Bitcoin Core developers generally don’t consider this edge case of a very long block reorganization as a realistic problem, and/or they believe that this would be such a big problem that a buried soft fork would comparatively be a minor concern. However, van Wirdum and Provoost explain that not everyone agrees entirely with this assessment.
Toward the end of the show, van Wirdum and Provoost touch on issues like whether soft fork activation logic itself should be considered a soft fork, and whether soft fork burying logic should be considered a consensus change and/or require a Bitcoin Improvement Proposal (BIP).