A Yisroel wishing that he were to be a Kohen, is a wasted wish, akin to a תפילת שוא [Mishnah (Berachos 9:3), Shulchan Aruch (OC 230:1)], as this is something that's impossible for a Yisroel to ever be, due to his lack of Kohen lineage.
However wishing and striving for those spiritual things that are attainable to him is a worthy endeavor.
Just as with material matters, most people generally strive to improve their lot, so too, with regard to spiritual matters, people should also strive to improve their lot.
The Talmud (Makkos 10b) teaches:
בדרך שאדם רוצה לילך, בה מוליכין אותו
"Along the path a person wishes to proceed, on that path he will be led."
If a person shows Hashem that he sincerely wants to accomplish more spiritually, and that is the path that he would like to take in life, then Hashem will see to it, that his wish will become fulfilled.
כל המקבל עליו עול תורה, מעבירין
ממנו עול מלכות ועול דרך ארץ – If a person takes upon himself the yoke of Torah learning, then from Heaven, they take away from him the yoke of other obligations, which will give him opportunity for learning (Mishnah, Avos, 3:5).
If something so important as spiritual growth is attainable by every person, as is indicated by these sources, shouldn't they wish and strive to attain it?