You would never really want to just go ahead and sleep directly on top of a core mattress. Think of all the grime and dirt and sweat it is likely to absorb out of you sleeping directly on it. Then, think of how hard it is going to be for you to have it cleaned up. It is best to have a topper added on top of it as toppers are thinner and are easier to remove. They are generally easier to clean and wash too. Also, when the time comes when they are way beyond redemption of washing or cleaning, getting them removed and having them replaced with a new one is going to be less expensive than the price of a new mattress.
Do buy the right toppers for this purpose though. You have to understand that there are all kind of these toppers in the market-size, shapes, dimensions and all. Make sure that you get the ones that will exactly fit the kind of core mattress you have at home. If you can, you may even choose to get them customized a lot of people do so just so they are sure that their topper is perfect for their sleeping needs.