Not at all.
There are plenty of things you can do with static websites, especially given you can have site generators and/or can write javascript by hand too (shock!).
For example if the requirement is to have website editable by non-programmers, that's where static site generators shine. Sure, one has to press "deploy" button and wait a minute before changes are visible... but you get to keep all the features of static pages, like trivial scalability and very high security and availability.
Even if you have to have dynamic functionality (like a shopping cart), there is no need to do the whole website dynamically. Sure, have an API server which may even render the cart page, but the rest of the website can be fully static, maybe with a tiny bit of javascript to render the "number of items in the cart" icon.