I think that we should allocate our money into 5 categories.
1. Necessary expenses. I am talking electricity bills, food, school fees (if you are studying or have children), housing, healthcare, and transportation. I believe this group is where most of our money goes because we basically can't survive without these things.
2. Emergency fund. In cases of emergency, we should be able to get some money for it. Especially in countries where healthcare is not free, we should be prepared to pay if ever we get into accidents or we get sick though hopefully it never happens but still we have to be always prepared either way.
3. Savings. Some people save up for specific things like buying a better house, a better car, getting your kid into a better school among other things. Some people may just save for the sake of having money to pull for emergencies. I think emergency money and money I want to use into building a new home should be separate.
4. Investment. Aside from our day jobs where we get most of our money to pay for our necessary expenses, we should invest in assets to make our money grow. This could be gold, real estate or cryptocurrencies.
5. Luxury. When I mean luxury, I do not actually mean it has to be expensive. But I say luxury because there are things that we do not need but still want to have or experience like traveling or eating at a good restaurant. I believe that even though we should be smart in finances this does not mean we have to completely deprive ourselves of enjoyment.
Every person in the world wants to move from their current position to a better position. For this, the first thing that should be done is money management. And at the beginning of money management, it is crucial the analyze of income and expenditure. When a person's expenditure is less than his income, then the steps you mentioned will be ideal, not otherwise.
And when a person's income is more than his expenditure, then most people give priority to saving and investing rather than enjoying it. But from my point of view, it is not at all right as you said that a budget should be kept for luxury. Because if we review a little, almost all people in the society die leaving about 70 percent of their earned money unused. So a person must be equally interested or focused on luxury or enjoyment as well as necessary expenses, savings, and investments, which I believe will make him more active in his work.