There are certainly prominent writers who would disagree, but I believe punctuation is important.
Punctuation can give rhythm to a piece of writing, allowing the reader some breathing space, some thinking space. Short sentences can be emphatic. They can be punchy. If there are too many, it can become annoying and require too much repetition which also can become annoying. Overly long sentences can be confusing, as well as being difficult to write and punctuate correctly.
As for meaning, even a comma in or out of a sentence can make a huge difference to its meaning. This blog post gives a few examples of the importance of commas and other basic punctuation marks, as well as offering a few chuckles.
Have a look at this excerpt from James Joyce’s Ulysses. Warning! It’s a little racy. In the final 24000-odd words, there is not a shred of punctuation, not even an apostrophe! I’m not going to criticise such a respected writer, although I would point out that this extreme style can be quite exhausting for the reader, and possibly ambiguous, borne out by the number of reading guides that have been published to aid understanding of this piece.
In creative writing that’s fine, if that’s the author’s intention. It’s not such a good thing when the writing is for business or academic purposes, where clear, concise, unambiguous communication is important. It’s even worse if the topic is safety, or science, where there is no room for misunderstandings.
When writing for digital media, it’s important to bear in mind that attention spans are short, and few people will read something exhausting.
Here are a few more humorous examples of the difference a bit of punctuation makes. These are the best entries in a competition to write two thank you letters using the same words, but different punctuation, giving rise to different meanings