Actually for this specific question your country is a great example.

The answer is actually fairly simple. The countries that have much greater diversity in the languages spoken are the countries where those languages have been spoken for a long time. The reason English is quite uniform in America compared to how it is in England is precisely because English hasn't been spoken there all that long compared to England. The places which have the most notable diversity in the US are either the places which were settled earlier, or the places where the settlers had some additional background in common and brought aspects of that with them (e.g. Pennsylvania Dutch, Scandanavian influence in some places, Gullah...).

Prior to the arrival of Europeans in North America, the linguistic makeup was much more diverse than what you see in English varieties today. The same goes for places like Australia.

The other important factor, which goes along with the passage of time, is the significance of geographical barriers. Waterways and mountain ranges often play a major role in dialect divergence. For example the Yangtze River was the main barrier between Mandarin and Wu, and one of the most striking exceptions to this is a town north of the river which speaks Wu instead of Mandarin, because at some point in the past, the river actually changed course, before which time the town was actually on the south bank, not the north as it is today.

Distance or other barriers plus time leads to divergence. Contact plus time leads to convergence. All language varieties are doing both all the time, and whether one focuses on the divergence or convergence more is entirely a matter of perspective.

Wait another few hundred years and you'll probably see American English diverge a bit more, although things like standard language curricula do have an role in slowing this sort of thing down.