Isn't it true that the Presidency is the only political office that is directly elected by all votes in the country, while Senators are elected by individual States and Congressmen/women in individual Congressional constituencies (sometimes gerrymandered)??
Yes the "one person, one vote" principle give an unproportional power to elect the President to voters in the big states and cities and may not be "fair" to the small and largely agrarian States.
But it is very much in tune with the democratic principle of "majority rules". The checks and balance should come from the Congress, Senate, the Courts and the fourth estate, being the press. (Now also the "fifth estate", being social media and all kinds of bloggers etc.)
I know that this is a contentious subject and not likely to be solved here, so let's let it rest.
The remaining Kingdoms of Western Europe, (+ Japan, Malaysia and a few other countries) are all Constitutional Kingdoms, where the King/Queen is the largely ceremonial "Head of State", with no political power. (Different from the Middle East Kingdoms, Bhutan and Brunei)
BTW; Canada, Australia, New Zealand and a number of other former British Colonies (incl. Papua New Guinea) also have the Queen of Britain as their Head of State,
All European Kingdoms are governed by the Westminster System of Parliament, where the Head of Government is the Prime Minister, appointed by the King/Queen, but on the recommendation of a majority in the Parliament. If the Prime Minister no longer command a majority he/she will notify the King/Queen of his/her resignation and a new Prime Minister will be selected by the sitting Parliament by the same process. (No need for re-election)
The Upper and Lower Chambers of Parliament is selected different in different countries, mostly in an election by the people. Except in the UK, where part of the House of Lords are hereditary and partly appointed by the Prime Minister (Government) from among noted public and private figures, many of them former politicians as a reward for their past service. (This MAY be revised soon)
As to the arrangement in the European Union, it is a different matter.
With 28 (soon 27) sovereign states trying to make all decisions by consensus. A difficult task and a work in progress.
Sorry about this lecture, as I know that many here is fully conversant on how things work, in Europe and the rest of the world. But from my experience, I find that many Americans know little or nothing about things outside USA and just assume that things have to be the same, or similar, otherwise "no good".
Some I have discussed politic with believe that European style "Social Democracy" is a contradiction in terms; "How can it be democratic if socialistic"????