There is such a thing as oversimplification. Learning to use commas effectively indicates a higher command over the English language. Early in your education it may be acceptable to fragment the list, but there will come times when you are penalized for not using commas to effectively join the list. Leaving the list fragmented is rather elementary English, and you will be expected to use commas.
Furthermore, I believe that using periods in this case is actually a mistake. A period is used as an end, but your idea is continued through all of your sentences. As a result, I do not believe that it is correct to use a punctuation mark, which has the very definition of to end a declaration. Your declaration is continuing through your other sentences, and commas are perfect for linking.
Read through the page which I will provide the link to you for. It provides very clear explanations of how to appropriately use the comma, as well as plenty of examples to help you understand. You will quickly find that the comma is a very, very highly used punctuation mark, as you can probably already gather from reading my writing.
Using Commas