I disagree. I think the British Empire would still exist but its centre would be in North America. It would dominate the World.
No, I don't think that would have happened. Bureaucrats ran the British empire from London. There would haver been penal colonies and they would have allowed controlled settlement with the profits returning to Britain. Possibly prisoners would have been used as labour in the cotton fields instead of slaves.
The British Empire no longer exists largely because of the crippling cost of the First World War. Why did it cost us so much money? Because we had to buy material and we needed enormous loans to pay for the war effort. Who did we get the material and the loans from? It was the USA. The First World War caused an enormous shift of wealth from Europe to the USA which did very well out of the war.
Had Britain been running America, it would not have been a wealthy industrialised country so that situation would not have arisen.
Had the USA still been a British colony in 1914, the war would have been over in 1915. There would have been no Russian revolution, or at least, the communists probably wouldn't have won it. There would have been no fascist takeover and therefore no World War 2.
I don't think it would be so simple. Britain would probably have been stronger and richer, Germany, I suspect weaker and more chaotic, so maybe the war wouldn't have happened.
"
Give me your tired, your poor, your huddled masses yearning to breathe free" was the famous line from the poet Emma Lazarus - and it reflected the Open Door policy that the USA had since about the middle of the 19th century. They took millions of migrants from many European countries, and this might be considered as a 'safety valve' for European countries. Without the option of emigration these people would have been very receptive to the idea of revolution in their home countries.
Do you understand that Soviet Russia exists as a direct consequence of WW1? Do you know that Lenin only got to Russia in 1917 with direct help from Germany?
Yes of course, but Germany didn't create Lenin and indeed, Lenin didn't create Communism. Conditions were right in Russia for revolution and (in the real world) Lenin was the one who started the revolution, but in our imaginary scenario social social pressures would have been even greater and revolution might even have started in Germany.