As I understand it, the term “Republic” means the head of state is elected. The head of state may be the governor, president - whoever signs bills passed by the legislature into law. In the UK the Queen does, or in Canada her representative, the Canadian Governor General. In the French Republic, the president does - but that’s a weird system (trust the French!) where the president and prime minister both think they are the boss…In some places - Italy, Israel - the president is just a figurehead who signs the laws, like the Queen but elected.
In Canada, the term of Parliament was 5 years. There was some debate how long after that 5 years were up that the election had to be called; some considerations were debated in the Good Old Days about how long after the term of parliament expired before the election had to be called. Some suggested a year later, since at a certain point a budget might need to be passed - but that’s a whole separate topic about how the Prime Minister and cabinet could keep going on orders-in-council if no parliament was sitting to pass a budget. There have been interesting times, where an election results in a minority government, then it is defeated trying to pass a budget, and the next election takes a while, so the government went 2 years or more without a budget passing.
Usually, an election was called within 4 years; this is the discretion of the government. Going past 4 years was an indication the government was very unpopular and waiting for some sort of change in the polls. Recently the feds and most provinces have passed laws setting fixed elections at 4 years; although the prime minister can call the election earlier if he chooses, or if defeated in a confidence vote.
I guess it’s an interesting debate why the USA ended up with their executive and legislature different, while Canada and other Commonwealth nations (Australia, New Zealand) ended up with parliamentary governments. I wonder if the form of government in the USA was more based on the 1700’s style of government that was set up in their colonies, where the separate head of state (King or his appointed governor) governed and the legislature was more of decoration that might pass laws but the governor tended to ignore. This form of separate executive was installed also in the new US constitution so coped by future states.
By the mid-1850’s when the colonies began setting up serious government structures, the current form of parliament had evolved - the colonies were set up by the British government to mimic their style. Particularly, the tight control following the loss of the US colonies caused the revolution of 1837, at which time the British recognized that not allowing to colonies to run much of their own affairs would only lead to further revolutions.
So short answer - the full form of parliamentary democracy by the ruling party had not evolved in 1788, so the framers copied the “separate executive” model in their colonies. Once everyone was familiar with it, they all copied it.
I assume that a “governor for life” is possible, but given the US federal government structure I assume not too many states would be keen on lifetime offices for executives. The lifetime appointment of judges was an exception that ensured their impartiality and freedom from coercion - but like the Catholic Church has discovered recently, modern medicine has made “for life” a questionable job description for effective performance. I suppose you could concoct a “the queen is president for life” office, but no guarantee the heir gets elected after that. Plus, the heir could not be titled king or queen, since IIRC the constitution forbids awarding titles.