I have absolutely no problem with people going to nursing school specifically to gain admission into anesthesia school.
Nor do I. For some, it is just a means to an end, not borne out of a desire to be an RN at the bedside. That's okay, too.
My point is that life is full of uncertainties. The original poster is probably in his/her early twenties - a time of life that can be incredibly tumultuous. People fall in love, move across the country, have babies, get cancer - whatever. And the path from hard-science major to CRNA is a long one.
I am old, and I can only say that life has repeatedly proven to me that the people who best weather the ups and downs of life are those who have workable back-up plans at the ready.
In my mind, a biochem degree is a very attractive back-up plan.
I can say that as a person who did not complete their rigorous science degree. Left my junior year to obtain a BSN. Even years later, and in anesthesia school, I can honestly say that I wish I had finished that first degree - for many reasons.