As for why you need them, Wikipedia points out that because there's no concept of singular or plural (in general, excepting words like "私たち" for "we"), you may consider all Japanese nouns mass nouns. And with mass nouns in English you usually have to use something similar: ".. loaf of bread" ".. grain of salt". The "solution" is not the same in English as in Japanese (you still use "one, two, three.." in English), but still, you can't just remove it. For Japanese there are other ambiguities which are resolved by the counter system as well.

But yes, the counters.. that's one of the bigger stumbling blocks I ran into early on. Learned the numbers, yay! Then learned that I can't use the numbers when I want to say how many there are of something.. I limited myself to the few where I can, as in the counter for flat thin items like e.g. tickets. "にまいください"