Speed: Search-based puts a floor on how fast an interaction can be. "Button Syndrome" interfaces are a slow "hunt and peck" for new users, but experienced users can use them extremely fast, building up muscle memory so they don't even need to consciously think about the action they're taking. Imagine piloting an F35 with a search-based interface.
Discoverability: Buttons make it explicit what functionality is offered by the product... somewhat. Users may not know exactly what a button does, but they can make an educated guess based on labeling and context, and it gives them a jumping off point to experiment with it or find it in the documentation. With search-base interfaces, there's no natural way for a user to discover functionality they aren't aware of. Worse, a user may remember a function exists but forget the terminology, flailing in the search box guessing different terms.
This is not to say search-based interfaces are bad. There are mitigations to the downsides (the article mentions a few, like search suggestions), plenty of upsides to go along with it, and let's not pretend that button-based interfaces are all sunshine and rainbows. I only mean to say that these are things that should be considered.
I think the broader takeaway of the article is: Always be thinking holistically. It's important to consider how your users interact with your product as a whole, not just the individual features. Also important to consider how different users of varying experience with the product and the domain will feel with the UI—Often features for "power users" come at the expense of new users or vice versa.