This is also true for Web apps that do not have meaningful amounts of client-side code.
> Caching also works for client side rendering
There are obviously a lot of differences in how caching works, but client-side caching is generally strictly worse than doing so on the server. Using the e-commerce example in TFA, every browser has to maintain their own cache of the product information, which may include cache-busting things like prices, promotional blurbs, etc.
The server can maintain a single cache for all users, and can pre-warm the cache before any users ever see the page. Adding fragment caching, which allows parts of a page to be cached, a server-side caching strategy will typically result in less total work being done across the user population, as well as less work done at request time for each visitor.
As an extreme example, something like https://www.photopea.com/ would be a nightmare to use if it was server-side rendered. Or consider something like Google Maps. For things like ecommerce that are mainly focussed on presenting information I agree that client side rendering doesn't make a whole lot of sense. But that isn't the whole web.
Yes, and also how much interactivity is better served by a thick browser-based client than by a round-trip to the datacenter. In practice, many Web applications we encounter daily have relatively low interactivity (where something like Google Maps or the Spotify Web player score as "high"). And then they are implemented using thick frameworks that are frequently slower than a round-trip to a server for re-rendering the entire page was even as far back as 10 or 20 years ago.
Your extreme examples, plus applications like Figma, are absolutely places where I would expect to see thick client-side Javascript. However, most Web applications that we encounter frequently are more like e-commerce, blogs, recipe websites, brochureware sites, landing pages and the like that absolutely are primarily about presenting information. Using thick browser clients is a sub-optimization for most of those Web uses.