The structure of British government during the Hanoverian times was little different from what the UK has today. The monarch was effectively a powerless figurehead and executive decisions were made mostly by faceless very wealthy individuals in back rooms with the public face carried by a small set of charismatic figures who usually sat in parliament.

The US system was designed as a grand experiment. It made a certain amount of sense at the time: the country as a vast plantation steered by a benevolent master with policy set by wealthy landowners and businessmen who knew what was best for everyone. It was a system already in place in the Americas for generations and most national arguments could be hashed out at the club over some fine imported brandy or, for people like Franklin, some imported tea.

As far as it goes, there have been worse set-ups.

It's quite different. The House of Lords was much more powerful well into the 19th century. The monarch was hardly a powerless figure in those times. The Bill of Rights 1689 probably shifted the power more towards Parliament than before but the monarch was still very powerful. The UK system continues to evolve with notable precedents being set very recently like requiring a consultation of Parliament before embarking on military action and the limitation of prorogation powers.

The setup isn't the problem. The refusal to evolve is the problem.

I'd argue that it wasn't really the system in place. The system in place was one of states governing themselves. Before independence the states didn't really deal much with each other.