First I ask you: when is the last time you played a blockbuster hit which included mini games? There aren't many. You need to search for them.
Mini games in a design pitch is generally proof that the main game design sucks. The mini games were included to cover the entertainment holes of the original design. That is why mini games should never be included in a game design - mini games essentially admit fail in your main game design mechanics.
Of course IF you are a professional and know what you are doing mini games can be entertaining. In fact there are games just evolving around mini games (Mario Party, Puzzle Pirates etc.) or are just a tremendously successful mini game. But if you are a beginner designer please - please (!) forget all mini game ideas you have.