Do Wives have to Submit to their Husbands?

Muslims have to defend themselves against the charge that their religion does not prescribe good treatment for wives.  However, not having a good defense, they have a culture of finding fault with what the Bible prescribes concerning how husbands and wives should live.

Here is a verse that is often quoted:

²² Wives, submit to your own husbands as to the Lord, ²³ for the husband is the head of the wife as Christ is the head of the church. He is the Savior of the body. ²⁴ Now as the church submits to Christ, so wives are to submit to their husbands in everything. 
(Eph 5:22-24)

The first point here is that whether the wife submits to her husband is between her and God.
The second point is that there is no mechanism provided for husbands to cause wives to submit to them if they fear disobedience from them (that is, there is none that works by force).

The third point is that the verse above is followed by a directive to husbands:

²⁵ Husbands, love your wives, just as Christ loved the church and gave Himself for her.. 
(Eph: 5:25)

What did Jesus do for the church?  He died for the church.  That is a lot more than what is being asked of wives.