Children and youth don't have temple recommends, either. There are TONS of worthy members of the church who are not qualified to get a TR due to age or other ridiculous constraints.
The fact is that the church LAW was to have PUBLIC weddings for years. Then, BOOM, along comes polygamy. When polygamy was secret those were performed in private for obvious reasons. Monogamous weddings were STILL held in public per the requirements in the D&C.
Let's read from the Article on Marriage that the church voted on and agreed to abide by in 1835, shall we?
According to the custom of all civilized nations, marriage is regulated by laws and ceremonies; therefore we believe that all marriages in this Church of Christ of Latter-day Saints should be solemnized in a public meeting or feast prepared for that purpose, and that the solemnization should be performed by a Presiding High Priest, High Priest, Bishop, Elder or Priest, not even prohibiting those persons who are desirous to get married, of being married by other authority. We believe that it is not right to prohibit members of this Church from marrying out of the Church, if it be their determination so to do; but such persons will be considered weak in the faith of our Lord Jesus Christ.
Marriage should be celebrated with prayer and thanksgiving, and at the solemnization, the persons to be married, standing together, the man on the right and the woman on the left, shall be addressed by the person officiating as he shall be directed by the Holy Spirit, and if there be no legal objections, he shall say, calling each by name: 'You both mutually agree to be each other's companion, husband and wife, observing the legal rights belonging to this condition: that is, keeping yourselves wholly for each other, and from all others, during your lives?' And when they have both answered 'yes,' he shall pronounce them 'husband and wife,' in the name of the Lord Jesus Christ, and by virtue of the laws of the country and authority vested in him. 'May God add His blessing and keep you to fulfill your covenants from henceforth and forever. Amen.'
The clerk of every church should keep a record of all marriages solemnized in his branch. All legal contracts of marriage made before a person is baptized into this Church should be held sacred and fulfilled.
Inasmuch as this Church of Christ has been reproached with the crime of fornication and polygamy, we declare that we believe that one man should have one wife, and one woman but one husband, except in case of death, when either is at liberty to marry again.
It is not right to persuade a woman to be baptized contrary to the will of her husband; neither is it lawful to influence her to leave her husband.
All children are bound by law to obey their parents, and to influence them to embrace any religious faith, or be baptized, or leave their parents without their consent, is unlawful and unjust. We believe that husbands, parents, and masters, who exercise control over their wives, children and servants, and prevent them from embracing the truth, will have to answer for that sin.
The Article on Marriage remained in the D&C until long after the saints got to Utah and began to practice polygamy in public. They were in direct violation of their own law.