Did Islam permit the marriage of a girl once she reached puberty, regardless of her emotional and mental development, or is this specific to the physical aspect and her ability to conceive? And does the same apply to males?

A father is permitted to marry off his young son or daughter for an overriding benefit, such as the marriage of the Prophet, peace and blessings be upon him, to Aisha when she was young. Some scholars, like Ibn Shubrumah, disagreed with this, holding that marrying off a young girl is absolutely impermissible. The correct view is that a father should not marry off his daughter until she reaches puberty, and once she reaches puberty, he should not marry her off except with her consent, unless he sees a benefit in marrying her to a suitable match whom he fears losing. As for consummating the marriage with a young girl, it should occur when she is able to tolerate intercourse. The ruling regarding a young son is the same as that for a young daughter in considering the overriding benefit. The guardian or agent must choose what is best for his ward or client.