You can find a lot of free cartoons for kids on the Internet - just go to Youtube or some other video streaming website. For example, you can watch "Everything's Rosie" compilation on their official Youtube channel or on the BBC website. The main advantages of this approach are, of course, the price (or, rather, the absence of price) and the fact that you can start watching almost immediately. Nevertheless, many people still prefer to buy cartoons. Why? Let's consider the advantages of buying over streaming:
First, if you purchase the cartoon, you can watch at any time, it becomes yours forever. No one can guarantee that the YouTube video will be available tomorrow and that the website of the TV channel will not delete your kid's favourite episode. When you buy the cartoon, you can watch it again in a year or two or whenever you like, even if you deleted it from your hard drive, because usually the videos can be easily restored using the website where you purchased it.
Second, you can buy the whole season of your kid's favourite cartoon. Video streaming websites often have only individual episodes, not the whole seasons. If your children love binge-watching their favourite shows, buying is the best option. You can also buy a cartoon video collection for your kid, for example, a "Cute Animals" collection from "Everything's Rosie", if they like a certain genre.
Of course, everyone decides for themselves whether to spend money on cartoon videos for their kids or not. It should be noted that the price is not so high - for example, the whole season of "Everything's Rosie" costs just £14.99 (for more than 4 hours of videos). Before deciding whether to buy the cartoon or not, you can watch some episodes for free on video streaming websites, and if your kid likes it, consider buying the whole season to be able to watch the episodes in a row and rewatch them at the convenient time.