I think part of the reason its around the 3BB mark is for stealing from the blinds. The higher your raise the more often the button steal has to work to show a profit.
Ideally you would like to raise to 2-2.5BB as this gives you the best
odds when stealing (thats based on the idea that most people have a calling range which they will call anything between 2-5BB with regardless)
However this means that your value raises on the button also have to be very small too, otherwise you are just announcing you have a good hand PF, when infact you want to try and get an extra bet from them.
So 5BB is great from a value point of view yet poor from a stealing one as now your steal success has to be much higher.
2BB is great from a stealing point of view but the trade off is the value you lose when you have a good hand.
So a one size fits all bet size is 3-3.5BB. Its small enough that your steal success doesn't need to be ridiculously high to show a small profit, yet its high enough to get some value (although not max values) from your better hands.