That's a great idea. My housemates all use a notepad and pen to write their weekly/monthly budget out and like you say they seperate that into different categories. Their bank should provide a form for them to write in their budget and then like you say they should then get alerted when they are about to go over their budget.
This is partiuclarly the case when someone approaches their overdraft limit. In England if you go past this limit you get charged £38 even if you a few pence past the limit. This has been heavily in the news over here and banks should help customers by alerting them when they get near to that limit.