If the Brits had never lost the US, it would now be a similar country to the other anglosphere countries i.e. much more stable and normal with a parliamentary system. Wouldn’t necessarily not have a president - there are former colonies with Presidents but they still work with a parliamentary system. The States could still have their own governments and have their own rules, and a federal government too (like Australia). You could still celebrate an independence day - when you severed ties from being British subjects (like in Australia - also same day the first fleet arrived in Botony Bay and set up the internment camp so it’s “invasion day” to the First Nations folk understandably) or when you signed a treaty with the indigenous folks (NZ) or when you decided to become a confederation of states (Canada). Honestly it would’ve been great to have kept the US in the British Empire for longer as you’d have kept the British sense of humour.
If the Brits had never lost the US, it would now be a similar country to the other anglosphere countries i.e. much more stable and normal with a parliamentary system. Wouldn’t necessarily not have a president - there are former colonies with Presidents but they still work with a parliamentary system. The States could still have their own governments and have their own rules, and a federal government too (like Australia). You could still celebrate an independence day - when you severed ties from being British subjects (like in Australia - also same day the first fleet arrived in Botony Bay and set up the internment camp so it’s “invasion day” to the First Nations folk understandably) or when you signed a treaty with the indigenous folks (NZ) or when you decided to become a confederation of states (Canada). Honestly it would’ve been great to have kept the US in the British Empire for longer as you’d have kept the British sense of humour.