You are asking more then one thing here.

1. Why doesn't the Print module have an option to save as TIFF
2. Why does the print module exist
3. What advantages does TIFF have over JPEG

Answers below:

1. It is anybody's guess who isn't on the development team, but it has been requested as a feature to add in the future(here and here).
2. Its main advantages are to setup contact sheets and customized layouts via templates
3. See existing answers here: Should I use JPG or TIFF for high-quality prints?

You are asking more then one thing here.

1. Why doesn't the Print module have an option to save as TIFF
2. Why does the print module exist
3. What advantages does TIFF have over JPEG

Answers below:

1. It is anybody's guess who isn't on the development team, but it has been requested as a feature to add in the future(here and here).
2. Its main advantages are to setup contact sheets and customized layouts via templates
3. See existing answers here: Should I use JPG or TIFF for high-quality prints?