Why are the Abrahamic religions so adamant about covering the head? Was there some basic, practical reason for it?

I've never been convinced about the "practical" reasons behind a lot of the religious laws. We can explain the Jewish and Muslim bans on pork like that, but what about the Jewish bans on crustaceans, eating milk and meat together, not shaving your beard, not shaving the corners of your head, etc.? The Jewish laws in particular appear to be more about social differentiation from neighboring groups, i.e. they do that so we can't (Sikh laws are at times quite similar in intend), than about anything so practical as health.

As for the hair, this seems to be caught up in classical ideas about female modesty. I don't know if there is a definitive study on the three, but look at this excellent analysis of Greek and Roman (pre-Christian) customs about head coverings for women, with pictures. It is clear that in parts of the Greek world, and among certain Roman classes, heading covering was just what respectable women did. The Greek language historian Plutarch, in his Sayings of Spartans, written in the first century CE during the Roman empire long after the Spartan peak, records that Spartans (at least used to) say:

"When someone inquired why they took their girls into public places unveiled, but their married women veiled, he said, 'Because the girls have to find husbands, and the married women have to keep to those who have them!'"

I do not know of any reference to female head-covering in the Torah or the other books of the Hebrew (we can tell from vocabulary largely written before Greek and then Roman influence), but in the Talmudic period, written after the Roman destruction of the Temple, we see clear statements that women not covering their hair is grounds for divorce. Well, the wording is actual ambiguous and might mean just their hair needs to be tied up (braided, or perhaps tied with a headband), but it has generally been interpreted by later commenters as meaning covered. Clearly, the sort of dress is considered immodest and not what a proper woman would go about doing. Philo, a Hellenized Jew writing in the first century CE (before the Talmud), mentions women's head coverings as a "symbol of modesty" rather than a religious commandment (cited in the source above).

It seems that in Christianity and Islam, there are similar assumptions that head-covering is just what modest, respectable women wear. The main Christian text is 1 Corinthians 11:6, but the context makes it clear that this is about what is proper and respectable attire for prayer. In Islam, there are several commonly cited texts for head covering, both in Quran and Hadith, though the Quranic ones I believe are ambiguous as to actual hair covering (rather than general modest dress) and the Hadiths someone has told me are perhaps directly specifically at Muhammed's family/during prayer (who had to be modestly covered always because people were always over praying and they shouldn't be distracted), though I haven't spent a tremendous amount of time looking into the issue and can't remember what the texts actually say off the top of my head.

I'll point out that these are all about WOMEN covering their head. Jewish men covering their head is for an entirely different reason (see this article for a good historical review of the yarmulke/kippah, but in short it's a "reminder of Heaven above"). Christianity specifically forbids men from covering their heads during prayer, and some schools of Islam regards male prayer caps as praiseworthy but not at all required. In some other Abrahamic religions, like I believe Druzism and Mandeanism, I'll point out that many other Abrahamic religions (Baha'i, Karaite Judaism, Ras Tafarism etc.), there is, to my knowledge, no compulsion for men or women to cover their heads. Sikhism, on the other hand, has a tradition for men to wear Turbans, but this is not a requirement (the requirement is for men and women to never cut their hair); similarly, Ras Tafari men traditionally wear "crowns", but I am not sure that's seen as requirement for Ras Tafari men or just a praiseworthy traditional action.

Interestingly, while most traditional Jewish sources demand that married women cover all or part of their hair, some, like the famous early 20th century Baghdadi rabbi, the Ben Ish Chai, at the time probably the most important rabbi in the Sephardic/Mizrahi Jewish world, argued that this was not required in areas where modest did not cover their hair. See here.

tl;dr: I think the best reason is that when the laws and traditions of Islam, Christianity, and Judaism were written down, in the Mediterranean World, there was a clear sense that respectable, married women covered their hair outside of the home. This got recorded as law, even as fashions changed. In Christianity and especially Islam, there is debate about whether this what women always must wear, or only what they must wear during prayer. There is similarly debates about whether the laws demand modest dress or specific forms of modest dress. Some, like many Christian groups and the Ben Ish Chai, argue that the laws are about the behavior of modest women so it's dependent on local practices of modest women, while others declare that the laws define the behvaior of modest so are context independent.