Would education be better if there were more projects instead of exams?

Rather than asking students to memorize information for the possibility of it being on a test, we instead form the education system around giving students nontrivial tasks and projects to complete.

For example, instead of giving students a bunch of formulae for geometric areas, you give them a bunch of geometric shapes with their areas and ask them to find a relationship.

Or instead of giving a bunch of surface-level historical information, students go in-depth into some historical event or person and present a project on the causes and effects, how the past shaped their actions and how those actions shaped their present and how the consequences shaped the future.

Science would be more experimental, rather than formulaic. Students would re-derive basic principles, only they would actually know personally how the formulas work, instead of "trust the science".

Literature would be more discussion based, not memorization based. More book reports instead of summary quizzes.

Schooling would be more active, interactive, effective, and would actually instill learning instead of mindless fact grinding.

Thoughts? Why is this not being done?