There are always some trade offs, as bottom line - attractive offers are not free.

As you have mentioned, the initial HP will harm you short-term until it can be removed from your report. However, the early closure has a bigger impact to AAoA. Since AAoA is taken as an average, the more frequent and aggressive you are doing this, the more extent of the long-term damage. Don't forget the age of your existing cards will reduce this long-term damage. That's why if you just begin, you should try to convert your accounts instead of closing to preserve the AAoA.