Is intercession considered a necessary means to be taken when applying for something, despite the availability of the required conditions for those in higher positions?

There is no contradiction between the heart's reliance on God and the adoption of legitimate means. However, it is not permissible to adopt illegitimate means. The ruling on adopting means varies depending on the cause. The ruling on mediation depends on whether injustice results from it or if you are not qualified for what you are undertaking. If injustice results or if you are not qualified, then it is forbidden. But if you are qualified and no injustice results, then it is among the legitimate means.