Some people are problem solvers and actually derive enjoyment and other personal benefits from troubleshooting problems, coming up with solutions and executing on them. Let's refer to them as "quarterback" type of investor. These may be the "Bucket 2" people. In my opinion the quarterbacks happen to be some of the most impressive investors I have encountered. They are usually above average intellect, successful other aspects of their lives, and extremely confident in their capacity to handle almost anything that comes their way. When an issue arises, my clients who are quarterbacks really can't help but dive in and would naturally have a hard time outsourcing the results (winning) to someone else because really they are just built for it. With the game on the line they want to call the play and throw the winning touchdown. They would even catch the game winning touchdown if they could. They may justify this with the cost savings or control arguments that you have read from responses above, but the truth is they get way more personal value than the cost savings or control alone.
What the "Quarterback" does not usually understand is that in this role they are exchanging time for money(or cost savings) instead of exchanging time for equity. The quarterback has to play and play well if they are to win. If he does not play or does not play well the team cannot win or is less likely to win.
Someone who exchanges time for equity would be the coach or even the owner of the team. (Bucket #1 people and some Bucket #3 people who eventually move to Bucket #1) The coach has a result that he needs to attain (winning) and invests time into the quarterback to get the result. The coach cannot be the one to throw or catch the game winning touchdown himself but directly benefits from the result with equity. They equity for the coach could be a annual salary that most people could retire from after one year or even status of the position. The coach may not even be the best example of time exchange for equity. The owner of the team may be investing money and time in the finding and hiring a coach but is gaining equity from attaining the result (winning).
I apologize to the non sports fans who will not relate but as you can probably tell I really miss not having sports.