If you're a coder, you understand this extremely well, implicitly: You set up your IDE fonts and colors in a way that helps you see through the code. You don't want to be looking at letter forms when you're trying to grok something.
This is also the job of designers: Creating typefaces and layouts so that people see through the text, to the meaning.
Leaving your website in the system standard font basically screams "I do not give a shit about what is written here" and also possibly "I run a quacky conspiracy website" and me and most people will scroll past your writing as quickly as possible.
But there is no font that has no connotation. Every font has subconscious meanings to readers. Knowing what these are is important. Times New Roman screams, "I'm still using Windows 98". Whereas Comic Sans screams, "I work in a shitty real estate office". Simple examples. But the art is much deeper than that, because Optima Sans and Univers read very differently to the general public in ways that I could spend another few pages explaining. Every choice you make with type implies something that sits as a layer on top of the text that's written in that typography. But if you do your job well, you make the artisanship transparent, and allow the content to shine.
This is why typography is a bit of a black art, and why it's powerful. It subtly influences people in ways they don't notice and don't understand, while they're absorbing written information. Dig:
https://en.wikipedia.org/wiki/Antiqua%E2%80%93Fraktur_disput...