I understand exactly what you are saying here, however, there have been several times in my life where buying a coffee here or there will break my budget. I know that's a level of poverty that most people on HN have never experienced before, but it's a reality for many people.
You don't really ever want to go into panic mode. Living on a very limited budget is not the end of the world. I actually chose my lifestyle. I had this idea that there are 2 ways to be rich: make more money than I need, or need less money than I make. Sometimes the second one involves a lot less stress (which is admittedly quite difficult for a lot of people to believe).
If you are on such a limited budget, it is quite important that you know whether or not that coffee on Monday means that you aren't going to eat on Sunday. At the same time, if you do have some wiggle room, it's quite important to treat yourself occasionally.
What is important to track as your expenses has nothing to do with absolute value. It has to do with the value relative to your total budget. If nothing you buy costs more than $5, then obviously you are going to track smaller values. On the other hand, one of the huge advantages of having no money is that it doesn't take long to count it ;-)
So I would rather say that if you need to track down to the level of individual dollars for a personal budget, something like GnuCash is probably not the appropriate tool.