The "free" States wanted not to count slaves AT ALL for the purpose of congressional representation. The "slave" states wanted to count everybody equally (slave or free), with the probable exception of Indians (who nobody wanted to count).
Perhaps the purests would have not ratified the Constitution and continued to live under the Aritcles of Confederation. In that case perhaps the British might have won the War of 1812 and reacquired some or all of their former colonies and the United States cease to exist. The purpose of the compromise was to allow the Constituion to be ratified and create a federal structure that could better protect the states from foreign empires that desired expansion of their holdings in North America and weakening or destruction of the United States.