No, it is not important to “fight” with your spouse. It is normal and important to disagree with your spouse. Fight and disagree are not the same.
Your entire post is filled with patriarchal language. Let and wife should never be used in the same sentence. Letting someone do something is for inferiors. Parents “let” their children do things. The boss “lets” you do things. It is not a word that belongs in marriage.
Silly little things aren’t things to take a stand for. That’s how compromise works. You give on the “silly” things so you can take a stand , respectfully, on the big ones. Unless your daughters body is a “silly little thing” of course.
I’m sure you did not anticipate the responses you are getting from women about the word “let” as you used it. That attitude often leads to divorce. Not right away, no. But after enough years of it. I hope you’ll think about your language. Trust me, your daughter is listening. Even as a baby.