Should I submit FAFSA even with high EFC?

Check with your school.

For Purdue,

To be considered for these scholarships and grants, you must file a FAFSA by the University’s priority filing date,

Many Purdue colleges have need- and merit-based scholarships they award to students admitted to their programs. To be considered:

Submit a Free Application for Federal Student Aid (FAFSA) to Purdue West Lafayette by Dec. 15.

This is on the page listing the automatic National Merit scholarship and all merit scholarships.

Merit awards should not be affected by income/EFC, pretty much by definition. Whether a school actual does this, or one believes a school’s statement that it does this - YMMV, I suppose.