Your system sounds simpler but more rigid than mine. In my system, everything is a negotiable trade off. There is not static bills and savings to set aside, there is a trade-off between those things and spending. If I want to spend more on groceries or socializing or vacations in some period of time, that is just a trade-off against all the other things in my budget. Maybe I'd rather find ways to lower my bills than my spending. Maybe I want to save less in some month so that I can spend more on something that will bring us more joy that month. It is easier to make these decisions on trade offs with good visibility into all spending and saving.

But I would also suggest that it seems like you're actually doing the thing you said you don't understand why people do. You have a budget, it just has a relatively small number of categories. But the answer to your question is that people do this for the same reason that you do your setting aside of money for bills, savings, and spending.