A primary reason was to carry over the pattern from Original D&D (1974) and the first issue of the cleaned up Basic D&D (Holmes 1977 and then Moldvay 1980). That bonus structure was in the original game. (See @Badmike's answer for details).
Mentzer's Basic/Expert/Companion/Master/Immortal Dungeons & Dragons (1983, aka BECMI) was a reorganization and improvement to the original game that was less complicated than Advanced Dungeons and Dragons (AD&D 1e) - the two were parallel product lines that replaced the 1974 original game (in different styles).
As a side note, the Holmes Basic D&D (1977) had in it a direct reference to Advanced Dungeons and Dragons as the "what you do next" once the characters got to the end of 3rd level - which is as far as that Basic Book went. It too had the same XP bonus structure. Moldvay/Cook Basic/Expert and BECM(I) decoupled from AD&D 1e. (A complete listing of D&D editions is here).
The rest of the answer is found in the AD&D 1e PHB
Original D&D, Holmes Basic, the Basic (B/X), the (BECMI) D&D edition that you cite, and AD&D 1e were all deeply interrelated. They are all built around the same OD&D chassis (that simply offered those bonuses without explaining why, see this answer by Badmike); the AD&D 1e PHB offers some of the why. Gary Gygax is that book's author; AD&D grew out of OD&D.
Here's the "why" for Strength.
Strength is the forte of fighters, for they must be physically
powerful in order to wear armor and wield heavy weapons. Therefore,
strength is the major characteristic (or prime requisite) of
fighters, and those fighters with strength of 16 or more gain a bonus
of 10% of earned experiencec(explained later). (PHB P. 9)
Here's the "why" for Intelligence.
Moreover, intelligence is the forte of magic-users, for they must be perspicacious in order to correctly understand magic and memorize spells. Therefore, intelligence is the major characteristic of magic-users, and those with intelligence of 16 or more gain a bonus of 10% of earned experience. (PHB P. 10.
The explanation for Wisdom, on the other hand, isn't as 'back portable' from AD&D 1e; that edition featured bonus spells for higher wisdom and lacks the clarity of the STR and INT "why" points. The pattern @Badmike noticed is consistent: encourage a player with a high prime requisite in a given score to choose a particular class. (That was by no means required).
Given the space restrictions and the 'rush' to publish OD&D, the "why" was never explained in the seminal volume: Men and Magic.
AD&D was the next edition published. In it, EGG expended a significant amount of text in explaining some things. (And more in the DMG, but he didn't explain everything).
By the time Basic was published, early 80's, this bonus had become axiomatic. Was the "why" necessary?
For those who cared, it had already been explained in the AD&D PHB a few years prior.
FWIW: if our once-active member ExTSR does drop by again, he can answer it with some clarity as the core author of that (BECMI) edition. (Not betting the rent money on that).
For further reading on both how and why Gygaxian design ideas - "Gygaxian Naturalism" is not the same as "realism" - strike so many contemporary players (and DMs, and game designers) as odd, Justin Alexander and James Maiszewski explain how deeply ingrained in OD&D, AD&D 1e, and BECMI that design philosophy ran.