I will go home.

I can't answer this question, but it may be left over from old English. I note that in Norwegian (a cousin from the Old English side), there are two forms of "home": hjem and hjemme. The former is used when movement is involved: "Jeg drar hjem." [I'm going home.] The latter is used when someone is stationary: "Jeg er hjemme." [I'm (at) home.] Similar constructions are used for the Norwegian words for "up" and "down".

Perhaps "home" is so basic to us, that our language treats it as a direction (like "up" and "down") rather than as a place.

According to this site, in the phrase, "I will go home," the word home is an adverb of place.

Other examples of adverbs of place are: "I drove south," "She jumped up"

The site explains it in more detail, but I wanted to give a brief synopsis for those who hate following links. ;)

https://www.englishcurrent.com/grammar/go-home-adverb-no-preposition/

Your analysis of home as an adverbial modifier rather than a direct object is spot on. In the sentence "I will go home," home functions as an adverb of place, modifying the intransitive verb go. This contrasts with noun phrases like the beach, which require a preposition (e.g., go to the beach).

Interestingly, home belongs to a special category of place-related words that can function adverbially without to, similar to abroad, downtown, or overseas. This pattern has historical roots in Old and Middle English, where certain location words developed an adverbial sense. That’s why we say "go home" but "go to the park"—not due to simple elision of to, but because home inherently carries an adverbial function.

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