I think we could be comparing the quantities without numbers:
Ex: If we have to compare John's sticks with James', then we could keep eliminating one on one from both of them, and the one who ends up first has fewer sticks!
If we need to compare something unmovable, then we can get ourselves the same no. of sticks and go on!
If we want to keep our eyes on something (say, sheep) then also we could've got ourselves the same no. of sticks and then we could check if everyone is here or not!
A shopkeeper, too, could've sold his items at a fixed price; he could've shown the price through the no. of sticks!
So, why did we need to invent some notations or this number system?
You are right, as long as you have to compare small numbers, number systems are not always required. Another concrete example is the following: if you want to know whether your students fit in a classroom, ask them to sit down and see whether some student is still standing.
However, there are many situations where using sticks (that is, a unary number system), is not convenient. First, if you have relatively large numbers: historically speaking, it is probably the reason why improved systems were designed. Next, elementary operations (addition, substraction, division, multiplication), which also occur in very concrete situations, are not convenient to perform with sticks. But it took centuries to arrive to the decimal systems and the binary system used by computers nowadays, so your question is not as obvious as it seems to be.