Nobody weighs a purchase against a monthly allocation.
Why the daily number is the one that changes behaviour
Monthly budgets are decided daily. Nobody stands in a shop weighing a purchase against a monthly allocation, because the comparison is too abstract to make in the time available. A daily figure is the right size for that moment: it is small, it is concrete, and it is obviously spent or not spent by the end of the day.
It also makes the middle of the month visible. Most overspending is not one dramatic purchase, it is a run of ordinary days that each looked affordable in isolation. Dividing by the days remaining is what turns that run into something you can see while it is happening.
