That's a catchy thing to say but if someone is making $350K a year and easily saving / investing six figures annually without a budget, telling themn they need a budget sounds a bit absurd. I'd say the further you are from being able to invest / save sufficiently for your long term goals, the more a budget will help you. Admittedly, not nearly as catchy.
For the people who need a budget, they would just run out of money completely before their next paycheck and either get kicked out of their apartment, or dip into their savings.
I'm in that situation. I'm fairly thrifty and don't spend much. But after looking back over my spending, I've realized there was enough useless crap that I could cut out. For example, I realized I was spending an enormous (to me) amount on lunches at work, though it was nothing fancy. It's just that I was working in a rather touristy / "rich" part of town, so aside from a pastry, everything was above €10. I started packing my own lunch most of the time and the cost went waay down for no discernible loss.
Bonus points for eating less and losing some weight, but that's a different story.
Or can save some hardness as you reach 55plus, when getting employed becomes harder but state welfare is still 10 years down the line.
An habit to budgeting helps because people aren't always top dogs.