I humbly submit the following.
Other NT references to our being rinsed/washed with water make it clear that this new-birth water is the word of the gospel (e.g., Eph. 5:26), a word through which we were powerfully birthed anew as firstfruits of his new creation (James 1:18), and the gracious activity of God in washing his people is a profound motif in Ezekiel, not only in chapter 36 but in 16 as well (a context against which Ephesians 5:26 may best be understood). It's true that in Titus 3 the regenerating, gracious activity of the Spirit is also referred to as a washing, but that is precisely how these themes come together in John 3 (both the sovereign, mysterious, powerful, life-giving blowing of the Spirit, as well as the washing), with Ezekiel as its proper background, a cluster of new covenant promises which was not properly understood by Nicodemus but really should have been, and this lack of understanding provoked Jesus to express astonishment, which is an important feature of John's narrative and a powerful aid to our understanding it. (I.e., what exactly was Jesus astonished that, as "the teacher of Israel," Nicodemus didn't understand? Something about baptisms or washings? Perhaps not.) In addition, it should be said that we would be remiss to consider both John 3 and Ezekiel 36 if we fail to press on to Ezekiel 37, where the sovereign, gracious, powerful regenerating work of God's Spirit continues to be proclaimed, described, and promised to the people of God, and, importantly, the way in which these promises are set within the context of the reign of God's King David, whose throne is everlasting, a clear reference to the saving reign of Christ, whose Spirit the Holy Spirit is, the Spirit he gives to his people, whose kingdom had broken into the world with his own incarnation and teaching ministry. All these passages (and more) inform and support and enlighten each other, and consistently maintain the sovereignty, freedom, graciousness, and above all, the startling power of God in his giving life to a people who were dead, a people on whom he set his love.