2 Answers

Every country has unique ways of dividing power. When looking at different countries, it is also important to remember that the same title may be very different. For example, in the US, the President is probably the most powerful single figure in the government. In Germany, the President is little more than a figure head. So, the relative power of the position matters a great deal.

That said, most countries divide power between multiple positions as a way of preventing one person from taking total control. If the power is divided among several positions, and then one person is able to hold all those offices, that really defeats the purpose of divided government. Allowing one person to hold all the positions would be the same as allowing them to be dictator, since they are basically in charge of approving their own actions.

For this reason, most countries that have both a President and Prime Minister require that the same person cannot hold both offices at the same time. In my opinion, this is a sensible protection.

Very true.

Ireland also has both  Prime Minister and a President.