If the Brits had given the Colonies representations, America would've grown like Canada, much more controlled. The United States in the 19th Century was a free-for-all, with little government interference.
Imagine how it would have gone for slavery in the Southern colonies. Jamaica, Barbados, Bahamas, and the other West Indian British colonies had their slavery stopped when Parliament passed the Emancipation Act in 1833... And they paid the slave owners about 1 billion Pounds Sterling for it.
Now how much more would it have cost them if they also had to pay the slave owners of Virginia, Delaware, Maryland, North and South Carolina, Georgia and Florida (which was a British possession they only gave back to Spain at the Treaty of Paris).
Would the colonists still press on beyond the Appalachians and settle beyond the Quebec Proclamation Line of 1763? Would the Southern colonists bring their slaves with them, as they did when they settled Kentucky, Tennessee, Alabama and Mississippi when it was the young United States?
Imagine that the Connecticut Yankee Eli Whitney still invents the cotton gin? Could Great Britain afford to compensate slave holders then?
Imagine the Southern colonists declaring their independence over slavery in the 1830s, and the Northern colonies fighting them along with Great Britain to keep them in the Empire?
Would Louisiana and all the territory of the Louisiana purchase become Anglo-American? What about Texas, Colorado, Utah, New Mexico, Arizona and California?
Makes one wonder how different things might have been, eh?