This is excellent advice that I encountered in formal writing classes, as a matter of fact. I would add that long sentences are not always bad. Short sentences are not always good. Mixing things up for variety is ideal. John Irving (who teaches creative writing besides being an acclaimed novelist) says readers get bored without even knowing it when sentences are all of similar length and feel. Keep readers on their toes, he advises. Throw them a long sentence they have to think about. Then follow it up with short, snappy sentences. Pay attention to cadence. Keep the words flowing in an esthetically pleasing way.

To his advice, I would add that on-line writers need to be aware of their medium. With many readers consuming stories on mobile devices, be aware of what your sentences and paragraphs look like on small screens.

Long sentences look much longer on a phone than they do on a computer screen. Long paragraphs can look intimidating on a phone. With few visible line breaks, the eye has a more difficult time following and keeping track. This can cause fatigue or stress.

So, breaking up long paragraphs can help keep mobile readers reading.

Breaking up paragraphs might not align to what you learned about constructing paragraphs in school, but that doesn't mean you shouldn't do it.