Rodgers wouldn't be picked to help win her state she would be picked because she's a women something the GOP ticket desperately needs against someone like Clinton. She's a conventional safe choice she's not Bachmann type crazy she's a Establishment mainstream pub who's acceptable nationwide.
Kelly Ayotte is too and she's at least a senator who could help in New Hampshire. As for women, they've also got Susana Martinez, Condi Rice, Nikki Haley, Kristi Noem (not qualified but no less so than CMR), Deb Fischer, and others, all of whom are at least as good of choices as McMorris Rodgers.
Ayotte's up for reelection in the Senate. The party may not want to risk it.
Susanna Martinez has left the impression she's not interested in national office. Otherwise, she would be top choice for Veep.
I think Condoleeza Rice is possible, but she's pro-choice. That's a much bigger deal than Portman's support for gay marriage.
Nikki Haley was elected Governor by four points in a very conservative state in a very good year for the party. That's not an indication of a tremendous political talent.
Noem has less political experience than Rodgers (three terms in the House in 2016 VS six for Rodgers, Four years as state legislator VS eleven for Rodgers, Rodgers is in the congressional leadership.)
Fischer will only have four years of experience in Congress versus twelve for Rodgers. She's also in her sixties.
There is always the possibility that the nominee gets along with one person better than another. Someone who looks good on paper might not be the best campaigner, or might not be the best fit for a presidential administration.