Using golden ratio it is a good practice, because it is a constant proportion, but at the same time it increase in exponential matter, becoming interesting respect to other proportions. You shouldn't feel compelled to use it, but it is a great guideline in defining a design project.
If you talk about modern, on the internet, you cannot just apply the golden ratio to a web designed page. You can apply it on graphic design, software or product design, and it is nice applied because it is a proportion that it is doesn't look boring.
The reason that you cannot apply to web design it is because, web design it is a flexible design and not static/immutable: text can change proportion, different monitor proportions, layout can change size, the disposition of paragraphs and images can lose the relation. Too many variables to take in consideration.
I saw websites done by good designers trying to apply it, but still users with a simple click or resize of a page can change the whole proportion losing the effect. So for me you cannot apply golden ratio to something that cannot maintain a static proportions. You can try, but the effort of achieving it, it is not worth the result.