In basic D&D Clerics' primal Stat is wisdom. But it does not effect neither turn undead nor their spells. So why do they need a high wisdom? Just for the exp bonus?
In older D&Ds, not everything is tied tightly into things written on your sheet. Assuming that it works like modern D&D and that you can bring in modern D&D assumptions about what matters most—what's on your sheet—is a common mistake that can lead to de-optimising a character. There are mechanics that only appear within the adventure notes, there are ad hoc situations that will be judged by eyeballing the PCs' stats or testing them with a d20 roll, there are monster abilities that trigger off PC stats.
Your stats, therefore, should not be considered merely a source of bonuses. Your stats are what you are capable of, just yourself, when all of your abilities, gear, spells, and friends are missing, damaged, irrelevant, or stripped away by misfortune or misadventure. They are what lies between you and the unknown when you're in dire straits. A cleric is known for their wisdom, so a less-wise cleric will always be at a slight disadvantage, but whether that matters and makes any difference when the chips are down is something you can't know until you're tested by adventure.
So yeah, you don't "need" a Wisdom of 15 compared to a Wisdom of 13, but that's not the point. When you write down 13, you are saying "I am not as wise as the next cleric." Similarly, a lower strength means you're not as strong. There's no such thing as optimising here, just making a statement and then living or dying by it. You're making trade offs, with neither being better than the other. After all, you can't optimise for what you don't know, and old D&D is all about venturing into the unknown to see if you can come back better off. You can optimise for the short-term mechanical bonuses that are immediately obvious, but that's not wise, that's just making a wager that you won't need the other stat more and higher later.
First, your question doesn't really fit the mindset that B/X embodies. Asking:
So why do they need a high wisdom?
is incorrect. Clerics benefit from a high wisdom but there is no reason in B/X you can't run a character with a wisdom of 3 as a cleric. You'll just advance slower than other clerics.
3.x and on have been games about playing optimized characters much more than earlier editions although the trend started with AD&D where the four classes needed a minimum of 9 in their prime requesites and gained special class related advantages (such as extra clerical spells). In fact, if you go to OD&D you get the following bit:
Name: Xylarthen Class: Magic-User
Strength: 6 Intelligence: 11 Wisdom: 13
Constitution: 12 Dexterity: 9 Charisma: 0
Gold Pieces: 70 Experience: Nil
This supposed player would have progressed faster as a Cleric , but because of a personal preference for magic opted for that class.
As SevenSidedDie has pointed out a lot of ad hoc tests of attributes were common when B/X was current such as roll a d20 or 3d6 under a stat.
The advantage of this is you can play a character against type without a mountain of mechanical penalties. A B/X version of Peter the Hermit, a very unwise holy man who was very influential in the First Crusade, would just advance a bit slower than a B/X version of the Buddha. A 3.x version of Peter would be unplayable.
I just browsed both books and although later editions have rules for primary attributes, the classic D&D rules seem to have only the experience bonus for high attributes. Neither turning, nor spellcasting, nor maximum spell level nor anything else is changed by high (or low) wisdom.
I seem to have overlooked the character sheet where it says that wisdom modifier is added to the saves against spells, wands and staves. I have browsed the books again but did not find it in the text. I do have a German translation though, so maybe it's an error.
In short: because the other stats had already been taken.
A fighter is obviously strong. A wizard is obviously intelligent. A thief obviously dexterous.
So...now, you have someone intelligent enough to look at the castle's map and notice that there must be an hidden room behind the throne, because there is something wrong with the rooms disposition.
You then have someone strong enough to move that damn throne away from its current position, even if with a lot of grunting and panting and sweating.
Finally you have someone else who is so dexterous to disable the trap on the secret door and unlock it.
Pity is everybody die, as there is no one wise enough to realize that jumping (metallic) weapons in hand in a room with the sign "Danger: High Voltage" is not a wise thing to do...
Older D&D was simple, straightforward, with few rules, and very evocative (or, you could say, very stereotyped): the warrior is stupid and strong, the cleric fight evil and cure people, the mage is lean and smart (i.e. a nerd), and so on.
To do this, to help give a strong feeling to every class, you need to assign them some specific trait that is unique to them and, in doing so, you give them traits that the DM could use during the adventure, too. So you end up having the strong one, the smart one, the agile one, and the wise one: in all it makes for a wide selection of attributes to build an adventure on. In a very effective way you are forcing players to use all attributes available, to build a more interesting party, and you are rewarding them for that (the xp bonus)
So, yeah, someone had to pick wisdom.