> the problem in my opinion is the concentration of power in one person.

Generally, a prime minister is less powerful than an executive president, often much less powerful.

> and the prime ministers or presidents job is to only manage that group.

On the face of it, that is the PM's primary role in a parliamentary democracy. Now, the complication is that, in many parliamentary systems, the PM has significant power over the ministers (either via the ability to directly appoint them, or via being the head of the ruling party/coalition/or various other means). But generally, the PM is less powerful in nearly all systems than, say, the US president; in particular the finance minister is often a separate semi-independent power within the cabinet.