If you decided to pick 1 Simple Problem with 1 Solution, you're absolutely correct. Clearly listing or identifying one problem that you can provide a solution for is simply better.
If you're wondering why it's better, it's because it makes you YOU.
Hypothetically, if you were the client, would you pick a guy who has many solutions for many problems or a guy who specializes in fixing ONE CLEAR problem that you have?
Obviously, you're going to choose the guy who specializes in fixing one clear problem that you have over the guy who generalizes about fixing everything. It makes you perceive them as more capable of fixing your specific problem than the guy who generalizes about fixing every problem.
Specialty beats Generality. Sell Clearly