The only reason why the electoral college even exists is because it is the status quo. If America had gained independence today, or in the last hundred years for that matter, we probably would have gone with the popular vote.
More likely, if you gained independence in the last hundred years, you would have ended up like other first-world former British colonies that gained independence since US independence: Canada, Australia, New Zealand. You'd probably use a Westminster system with an executive in the legislature and a weak presidential figurehead (that's assuming you still become a republic - merely obtaining independence, you could still end up like those countries with a Governor General, and the Queen as your Head of State).
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