The product indirectly tells you the criteria for accepting the risk as-is, but it doesn't give you any insight into how to reduce the risk. That's what severity and likelihood are for. You need all three together.
https://en.wikipedia.org/wiki/Risk_matrix
Take a look at this risk matrix. It's divided into cells that are each assigned a category. If you assigned numbers to it, you'd get conflicting results:
1. Possible (3) x Catastrophic (4) = Very High (12)
2. Likely (4) x Critical (3) = High (12)
In this case, 12 can mean either High or Very High. Therefore the category is more important than the product.
So basically, the product is only meaningful if the categories are defined in terms of it, which I don't think is common. Really, I should have said you need the category, rather than the product.