Given God said it is not good for man to be alone and created Eve for Adam, what is significant about the phrase “because you heeded the voice of your wife”?
God did not create woman to be a sexual tool or incubator for man, to make possible his 'sole function' of reproduction. God created woman because "it is not good that man be alone" (Genesis 2:18). Woman completes man just as much as man completes the woman; they mutually imply the other by virtue of their incompletness—as physical creatures with an animal nature—without their counterpart.
In this verse, Adam is upbraided for obeying the disobedient words spoken by Eve. He was not being upbraided for listening to his wife, that is, simply for the sheer act of listening to a woman. In this context, "the voice of" Eve was one calling upon Adam to violate the clear words of God, that's why "listening" to them (which here means proceeding to do what they call for) was worthy of condemnation.
Adam was not chastised because he listened to the woman, he was chastised because he listened to Eve instead of the command He had given him.
Both parties are equally valuable, they may have different roles in His plan but each wouldn't be able to achieve that without the other.
One of the values I was always taught was a reminder that He took one of Adam's ribs to make Eve, not a toe, so that Adam could step on her, nor his hair, so she could be over him, but a rib, so that both could be equal partners in the creation, which emphasizes the importance of family* in my opinion.
*Family as the concept of the union between man and woman and possibly children
Despite finding the question to be rather difficult to decipher, I get the impression from some of the comments that the OP is asking about this phrase because you have heeded the voice
“Then to Adam He said, “Because you have heeded the voice of your wife, and have eaten from the tree of which I commanded you, saying, ‘You shall not eat of it’: “Cursed is the ground for your sake; In toil you shall eat of it All the days of your life.” Genesis 3:17
This phrase occurs in other places in Scripture and it basically means to follow instructions. Here are some examples
“So Sarai said to Abram, “See now, the LORD has restrained me from bearing children. Please, go in to my maid; perhaps I shall obtain children by her.” And Abram heeded the voice of Sarai.” Genesis 16:2
The context is Sara telling Abram to sleep with her maid
“and said, “If you diligently heed the voice of the LORD your God and do what is right in His sight, give ear to His commandments and keep all His statutes, I will put none of the diseases on you which I have brought on the Egyptians. For I am the LORD who heals you.”” Exodus 15:26
If you obey God's Commandments then these will be guaranteed.
“So Moses heeded the voice of his father-in-law and did all that he had said.” Exodus 18:24
Jethro instructs Moses how to set up government over the people in Israel. And Moses listens to him
“No, my sons! For it is not a good report that I hear. You make the LORD’s people transgress. If one man sins against another, God will judge him. But if a man sins against the LORD, who will intercede for him?” Nevertheless they did not heed the voice of their father, because the LORD desired to kill them.” I Samuel 2:24-25
Eli’s sons fail to listen to what their father told them to do
So in light of this, God is saying to Adam, because you obeyed your wife and did what she told you to do, I am cursing the ground, and so forth.
This puts into light the fact that Eve actively instructed Adam to eat. It wasn’t Adam who initiated, it wasn’t Adam who was curious to eat, it wasn’t Adam that intended to eat. Eve was not silent, according to this verse Eve instructed Adam to eat. And God chastises Adam for obeying his wife rather than obeying God’s instructions not to eat.
This goes to show that the woman had exercised dominance over the man and the man in his state of innocence obeyed, to both their detriment.