My observation is it can make a difference. But usually only when the major is somewhat unusual and under-subscribed (a university with an undergrad program in Egyptology which last year had five kids graduate with that major) AND where the application clearly demonstrates a strong interest in that area (kid volunteered at a museum giving tours to 3rd graders, wrote a curriculum for middle schoolers on how to understand the ancient world, taught herself Sumerian to be able to reach ancient inscriptions).
Your D is in the best position to know whether her goals are specific enough, backed up by what she’s done and what she’s interested in, to make this possible.
Econ major- does her HS participate in the federal reserve challenge and did she make the team? Is she taking whatever econ courses her HS offers and did she do well in them? Got a letter to the editor published in the business section of your local newspaper?
That sort of thing. If it were just a question of picking an obscure major to “stand out”, it would be a cakewalk!