The six New England states are separate because they all had different founders and developed unique identities. Four of the New England states were their own colonies before the Revolutionary War. Massachusetts, Connecticut, New Hampshire, and Rhode Island each started as their own colony with its own charter from the English Parliament and king. This meant that they began with their own laws and local governments.
Massachusetts was largely founded by the Puritans, who sought to establish a colony with the goal of creating a Puritan utopia in the New World. New Hampshire actually was claimed by Massachusetts for some time, but in 1679, it received its own charter. Connecticut was settled by Dutch fur traders before the English arrived and therefore retained its old borders and identity. Rhode Island began as a refuge for Puritans from the surrounding region, as some in the surrounding region sought a more liberal and religiously tolerant society. Vermont did not receive its own charter and remained a disputed and sparsely populated territory, at times claimed by both New Hampshire and New York, until its statehood in 1791. Maine was, in fact, part of Massachusetts until 1820. It became its own state in order to preserve the slave state-free state balance, as part of the Missouri Compromise.
With all these different histories, societal structures, and political bodies, each New England state retained, and still retains today, its own unique identity. While they share certain common characteristics, they likely would not coexist well as a single political body.
In fact, from 1686 to 1689, they were combined with several of the middle colonies into the Dominion of New England. This attempt at unification was short-lived, because the various colonies chaffed at having their local authority and charters stripped away. The various New England colonies were simply too independent minded to combine with each other.
Even today, if you travel from one New England state to another, you will encounter different local laws and distinct cultural identities that set each state apart from its neighbors.