Hurr ibn Yazid
Al-Hurr ibn Yazid bin Najiyah Al-Tamimi Al-Yarbuʿi Ar-Riyahi ( حر بن یزید بن الناجیة التمیمي الیربوعي الریاحي) was the general of the Ummayad army dispatched from Kufa, Iraq to intercept al-Husayn ibn Ali ibn Abu Talib. The newly appointed governor of Kufa, Ubayd Allah ibn Ziyad, issued the command to guard all entrances and exits to Kufa in order to intercept al-Husayn for an oath of allegiance to Yazid ibn Mu'awiya ibn Abu Sufyan of the Ummayad dynasty. Al-Hurr ibn Yazid al-Tamimi al-Yarbu'i was ordered along with his 1,000 soldiers to sanction al-Husayn and his followers and bring them to Kufa.
This is a thoughtful question that shows reflection on the historical account.
Insofar as there is no answer mentioned in history books, it is not possible to give an answer.
If I were to guess, perhaps it would have aroused too much suspicion to bring water, or perhaps it was an emotional and sudden moment and he was not thinking about things, or perhaps some other reason.
Ayatollah Motahhari was of the view that it is not correct that they were without water for 3 days and nights. See https://www.al-islam.org/al-tawhid/vol13-no3/ashura-misrepresentations-d...
I don't think there is historical evidence that they were without food, however, the lack of water is much more dire.
God knows best!
There is not much biographical information available about Hurr al-Riyahi (and if someone presents a detailed biography with previously unheard-of information, you should question where they got it from and whether they got it from reliable sources).
This webpage is well-written and explains what is known about the background of Hazrat Hurr as well as the reliability of various reports about him: http://en.wikishia.net/view/Al-Hurr_b._Yazid_al-Riyahi
The webpage does not speculate on his age but given his military rank and position, the respect he was given, the maturity with which he conducted himself, and that he was said to have adult sons (whether or not that report is correct), I would guess that he was somewhere in mid-life, old enough to have passed the younger stages of life but not so old that he was weak or showing signs of aging.
We believe that every act of the Infallible is based on the complete wisdom which may not be available to us as our thinking is limited.
The wisdom behind the way of fighting the enemies in Karbala can be to avoid immediate collapse of the camp of Imam Husain (AS) looking at huge numbers of the enemies facing small number of believers.
It can be also to give more chances to the army of the enemies to reconsider their stand.
After all, the whole wisdom of that arrangements is with Imam Husain (AS) which aims definitely to serve the noble aims of Islam.