A tally system is effectively "lots of ones". Each "one" is distinct. Being able to distinguish between different "many"s is important, even if you cant think of the exact amount. 1 gram vs 1 kilo. How many children do you have again?
See also: Men at Arms by Terry Pratchett. There is a part where Troll Detritus (normally slightly less than human intelligence) is being frozen to death, but his brain works better in the cold, and can make the leap mentioned above. Mathematics ensues.