In most of the European Universities I know, research groups are created from the equivalent of Assistant Professors and the Principal Investigator is voted in some sort of election, where there are elections every 2/4 years. In groups with such profile I have usually seen that scientific output is low and that most of these members are not really motivated to do research and are only affiliated to these groups for CV and promotion purposes. But this is of course my personal experience, I do not state this is always like this. From the other side I know other groups that are created from scratch from somebody with a very good CV, who has a vision and ambition, and who gets all research group members not from Department colleagues but from funding he/she attracts. All group research lines are derived from her/his experience and CV and scientific output in this case and according to my experience, tends to be high. Based on your personal experience or factual evidences, what is the most optimal configuration for a new research group, the former or the latter or do you think there are other different configurations?
If you want to maximize the output, impact and success of a research group you have to increase the synergetic potential of the staff, set up good research questions, acquire funding etc.
The PI can be a genius, but if he is unable to identify good researchers for his team, researchers with complementary abilities and lead a team, then he will underperform. Extreme cases of such PI's are savants/prodigies (e.g. autism syndrome) with limited social skills.
There are nowadays companies who "rent" savants or people with special abilities in math/informatics to other companies to solve distinct problems, but taking care of the social integration and well-being of them by setting the right boundary conditions for such jobs. This is not very different in research groups, you often have persons with very special personality, interests and social/cognitive abilities.
The optimal configuration of your group will always depend on what the research group is investigating and what the existing team is looking like. You don't want to have only alpha-males on ship if you set up a team to fly to mars.
There are even studies what kind of staff number is ideal in distinct scientific fields, a particle physics group has from theoreticians to experimentalists up to technical employees a very different structure in comparison to english literature.
The question is rather how do you develop from the current group structure to a better one, going from zero directly to the best one is only possible in a hypothetical perfect world with unlimited funding :-)
I assume you are basing this on European model, so in my experience the groups based around some common interests are the strongest one because they have a vision that can lead group. Usually these are friends or couples, that succeed to attract funding making multidisciplinary team. In such a team everyone knows each roles and they keep each other back by making sure people are represented in publications in terms of authorship equally. I would suggest you to take a look on Research Gate lab profiles where you can see how members of particular lab are connected and what grants or projects they menage. In my opinion it is the best way to discover dynamic of a group and internal structure. Second things are Center of Excellences, they are now because of HORISONT2020 becoming more popular and are highly hierarchical. However primordial idea for their creation was done trough application of group or consortium of reaserchers and scientist, in there you can observe same things as in your question, however structure is maintained highly hierarchical. In my opinion best way to organise research group is around "friends and family" because you need to trust people in order to follow through with your agenda. I'm not saying that groups that are based around one person are bad, but due to increasing emphasis in academia on teaching, management and bureaucracy, alone PI in current European funding scheme structure can not survive.