But if traffic is high in the beginning of the month does this mean you should be allocated more budget? How much? Such an alarm doesn't really give you any insight into where the additional costs might be, or where/whether it's worth spending engineering time optimizing!
If you don't have a budget, then that's what you should establish first. If you can't get a handle on your budget, then no set of tools and techniques is going to save you.
The point is that the budget changes all the time for anything other than a simple application stack. If you're constantly experimenting and building new applications, you basically need to quickly glance at your daily usage to make sure you won't get a surprise in 30 days.
I've never worked at a company where the cloud budget fluctuated in the way that you are describing, and we certainly didn't run "simple application stacks." Costs and usage patterns are predictable. If you want to do whatever you want, costs be damned, then I'd ask why you're even bothering to be alerted about costs in the first place.