The 17th and 18th centuries saw a rise in the idea of Absolutism in some European countries, notably France, Spain and Denmark. Many people seem to think that absolute monarchy is just the default state of a country before liberal democracy, but in fact Absolutism was a deliberate ideological shift. Prior to this, most of these countries had quite powerful parliaments, although they were usually not elected by anything approaching democratic means. Absolutism focused on the idea that putting all responsibility in the hands of one man, the king, would avoid corruption and allow for more centralised, efficient and dynamic rule. Of course in practice this meant peripheral regions tended to suffer at the expense of the great and good fawning around the royal court in the capital, and absolutism was ended in most countries by the reaction of the French Revolution.
The WI I'm proposing here is of absolutism under a democratic system. This could be an elected monarchy or a republic with a very powerful presidency. The idea being that the electorate (which is assumed to be universal suffrage or very nearly so) elects an individual to be president (probably for life) and that, at least in the idealised form, the people are considered all to be equal, with no nobility or parliament.
Such a system deliberately rejects checks, balances, or constraints on the power of this one-man executive, prizing efficiency and centralism above such things.
Is there any way we could get a system like that in a given country?
Although the USA has, of all modern countries that could reasonably be called democratic, the most powerful one-man executive, I don't think a system like the one above would work in the USA or Russia: large, federalised countries would tend to be inimical to it for the reasons I mentioned above. However, in order for it to be interesting WI, it has to be adopted in a country that's at least a moderate power. I suspect something the size of France would be about the limit.
So, where could this system arise/