The advantage is stack simplicity. As stated in the beginning of the article, LiveView completely removes your need for any kind of API between your front and backend. It also makes it very easy (through JS hooks) to offload any interactions you want to the client if that makes more sense. But of course, if you end up offloading EVERY interaction to the client, you should be using a frontend framework--LiveView is very clear about not being suitable for every need--if you are building a super UI heavy app (like a text editor or painting app or the like), LiveView probably isn't going to cut it.
I will pay the cost of a round trip if (a) it simplifies my life and (b) the cost is low enough. LiveView simplifies interactive app development (for me). Since I can run my Phoenix servers close to people, the round trip cost is usually very low.
Now if you want to avoid round trips to the server for interactions such as opening a modal, you can!
There are at least two ways to handle this - Javascript hooks that let you attach JS to your DOM, or the light AlpineJS framework. The latter is a perfect fit for Liveview and it's part of the unofficial go-to stack name PETAL - Phoenix Elixir Tailwind AlpineJS Liveview.