It was how most people budgeted up until maybe the 1980s/1990s when being paid into the bank became more common. I love how people on TikTok who weren't even born then talk about this sort of thing as if it's something new and revolutionary.
People would get their wages in cash on a Friday and would separate it out to pay rent, heating, food and other essentials and if they were lucky, might have a small amount spare for a treat over the weekend.
I agree that it would be difficult to do these days as many places are card only but you could do a similar thing using different bank accounts and pots. This also has the advantage of less risk of loss/theft of your cash and gives you information about what you spend in your accounts/apps.
Once you've worked out your budget, you could have:
An account for monthly direct debits
An account/pot for day to day essentials like food, travel costs
An account/pot for annual and irregular expenses like Christmas, school uniforms, other essential DC costs, insurance, car running costs, white goods replacement etc
An account/pot for joint spending money if you're a family, so days out, food and drink out of the house
An emergency fund/longer term/larger expenses pot, eg to cover loss of income, car replacement, home improvements etc
And finally, once all the above has been covered, your discretionary spending money that covers personal non essentials, whether small regular ones, or bigger ones as and when.
But of course that takes away the opportunity to make a nice video about it.