Why did the Qur'an not make marriage mandatory for having sexual relations with the slave woman?

The Qur'an does provide permission for those who wish to marry slave women (4:27). Indeed, the Prophet had said that such marriages will confer a double reward. 'He who provides the slave woman under him with proper manners, provides her with the best education, then frees her and ultimately marries her will be given a double reward.'' (Bukhari, Muslim)
The guardian of the slave is the master whether it be a male or a female slave. The guardianship of the slave woman who is under a male master rests with that man. Even if she is to be married off, it is he who will have to carrry it out. It is also he who is to take care of all her affairs. It is for this very reason that there is not the need for the act of marrying her. In Islam, marriage is a contract that is solemnized by the guardian of the woman and the bridegroom. In this case, he is both the master and bridegroom. Then the marriage ceremony becomes irrelevant in itself.
The Qur'an instructs that the maximum number of wives for a man must be four (4:3). Let us suppose that there is a slave woman under the care of a man who has four wives He cannnot, in that case, marry her. If he is not ready to grant her freedom, liberation from dependence will remain for her a dream. She will then be forced to resort to adultery in her bid to satisfy her sexual desire. But since there is the law that the master can engage in sexual relations with her without recourse to marriage, a solution for all such problems manifests itself. It becomes possible for her to walk into freedom when she gives birth to her master's child. It will also be the solution for her sexual needs. In a society where slavery prevails, if a solution is not provided for such problems it will lead to a large scale erosion of values. Along with this, there will also be the problem of the children born from adulterous relationships. Naturally, they ,too,will end up as slaves. The end result of all this will be that slavery becomes entrenched as a system that can, is, no wise, be terminated.
In the case of Islam, however, the provision is made such that the masters are permitted to have sexual relations with woman slaves, whereby, within the span of a single generation, slavery is made extinct. If 'marriage' is made a condition for it, it is not possible then to obtain the results envisaged by Islam. Certainly, all masters would not be willing to marry their slaves woman Besides, it is impossible for those who already have four wives.