BillyGoat, the idea of the buffer is to enable you to budget an entire month's expenditure in one go, and be guaranteed you've got all the funds you need until the end of that calendar month. So if (like me) you are paid monthly in arrears on about the 27th of the month, this is far less significant than if you are (as many people in the US are) paid fortnightly. The bill cycle is still monthly but most people don't have a month's dosh on hand when preparing the budget.
As the mantra is 'only budget the money you have on hand', you can't pay all your bills based on cash you have in your current account, so have to leave the later bills in the month unallocated until you get paid again.
The UK/monthly version of this is that if you have bills that could fall either side of your payment date (i.e. some months the bill falls before, some months after) and you're not buffered you could be having to pay out two lots from the same pay packet, which can make a big dent in your income of course. So I can be buffered effectively by having a week's wages set aside so all of my August pay cheque goes forward to September, but the holy grail would be to have a month and a week on hand so my August pay cheque is untouched until October. That way I know I can pay all my September bills even if (for some reason) my August pay cheque turned up very late.
So it's not the buffer that helps you be less wasteful, it's the method itself, which makes you give every dollar (okay pound) a job at the start of the month, or as soon as it arrives mid-month. The method doesn't care how often you are paid or when in the month that is, you always budget for the calendar month.
More about the method here - it isn't the most straightforward thing to get your head round, it's worth watching some of the videos as they work through examples. It's well worth it, though, as it gives you a sense of control and mindfulness about money.