As to why married women cover their hair:
Rav Falk writes in his pamphlet Mitzvos Kisui Saaros that “The Torah requires a married women to conceal her hair from the eyes of the public in order to lessen attraction to herself.” (page 7)
He continues: “An unmarried maiden may attract attention to herself (within the boundaries of tznius) so that she is sought after and eventually marries (Ta’anis 13a and Kesubos 52b). Similarly, a man may look at a girl and take an interest in her appearance, chein, mannerisms etc. if he is considering her for marriage for himself or someone else. A married woman may, however, neither attract attention to herself (Kesubos 73a Rashi v.s. Sahara. See also Rosh and Ritvo) nor may a man take an interest in the appearance of an eishes ish, as she is unavailable to everyone but her husband.
For this reason the hair of a girl may be seen, whilst the hair of a married woman, which is naturally a major source of attraction to her, must be covered and hidden from the eye of the public. Accordingly, for a married woman to wear a head covering that easily passes as her own hair, defeats the very function of this mitzvah, since a man seeing her can think that he is seeing her own hair and be attracted by it, especially when he does not know who she is and whether she is married or not.
A similar but different reason why just a married woman must cover her hair is based on the verse “stolen waters are sweet” (Mishlei 9:17). Due to this phenomenon there is a special yetzer hora towards a married woman since she is an eishes ish (see Sanhedrin 75a and Avoda Zarah 20a). The mitzvah of kisui sa’aros was given to lessen attraction to such a person and safeguard Kedushas Yisroel. See Oz Vehadar Levusha, page 265 that in numerous places in the Torah hair is highlighted as a major source of attraction. Accordingly, by commanding the married woman to withhold from the public how she looks in her true hair, there is far less danger of a person being drawn to her and Kedushas Yisroel is guaranteed.
A natural looking sheitel is furthermore forbidden because of Maris hoayin (it appears that the person is sinning), as some observers will not be able to discern whether this woman has covered her hair or not.” (pages 7-9)