I'm doing it now. Whether it's a website, a blog, or a social page, web writing needs to be conversational. This isn't a doctorate thesis or a romance novel... Web content is succinct writing that keeps the reader in mind. It should be friendly, too!
Think about visiting a website to buy a sweater. We don't want to frustrate people with irrelevant rambling or disorganization.
Consider why a reader is on your page and then think about how to help the reader complete their goal. Draw people in and ask them to engage with you; active voice helps keep them engaged. Knowing the audience and applying that information is the most useful tool a good web writer can have.
Big words and long winded sentences might sound beautiful in Paradise Lost by John Milton, but we're not writing an epic poem and this isn't the 16th century. People today lead busy lives and eliminating stress for your readers is ideal. Help them to help you.
For an example of my web writing, check out this article I wrote for I Heart British TV about the representation of alternatively-abled and disabled people in the film industry.