The word "go" has lots of meanings besides physically moving to a place. It also means to change state ("the milk went bad", "he'll go crazy when he finds out") and to indicate immediate future tense ("I'm going to read this book now"). Not to mention some other less relevant uses.
Edit-preface: I am not a grammarian. I don’t know what the technical names for the different types of “to” are or if they are even recognized as distinct by experts in the field.
English is does indeed use “go” to mean “go do a thing”, but not with directional “to” (as in “go to the library”).
“Go run!”, “Go running”, “I’m going running”, and “I’m going to run” are all valid uses. (In that last case, the “to” is not a directional “to”, but is actually part of the infinitive verb “to run”, as in “I want to run”). However, you wouldn’t say “Go to run!” to tell someone to run.
"Go to run" could make sense with a causal “to” (“Go, in order that you might run”) but that separates “go” and “run” in to separate actions. Causal “to” is the “to” in “push to open” and “press F to pay respects” this is not the “to” in “go to sleep”
“Go to sleep” feels like it is in the directional sense, like "go to bed"
Edit: Now you’ve got me thinking. “Go to sleep” and “go to bed” are a little unusual . “Go to [location]“ without an article is usually reserved for proper nouns or pronouns (“Go to France”, “go to Curicó”, “go to Walmart”, “go to John“ “go to her”). When the location is a general noun, you usually use an article or a proper/pro-noun in the possessive form (“go to a restaurant”, “go to the party”, “go to Bob’s house”, “go to your room”). So what makes “bed” and “sleep” so special? The only other case I can think of at the moment is “go to ground” and that is different because it is an idiom, and the rule for idioms is “they mean what they mean”
Edit-edit: meals don’t use an article either: “to lunch”, “to dinner”, “to breakfast”.
Edit-edit-edit: AAAAAH! It applies to some other prepositions too: “in bed”, “at lunch”; but not “under the bed”. What is going on‽
Edit-edit-edit-edit: Causal “to” might be a use of the infinitive case?
Edit-edit-edit-edit-edit: “go to work” does not use an article either.
I think it's because the "to" in those phrases are part of "to sleep" not part of "go to". The "to" modifies the verb "sleep" to be an infinitive and the "go" is an imperative verb.
I think that's more that tener (to have) doesn't always mean a physical thing.
As an example in spanish they use tener for age. As in tengo 20 años literally is "I have 20 years" but it means "I am 20"
Or ten cuidado means "take care" or "be careful" but literally is more like "have care". Both phrases use tener in a nonphysical sense in the same way as in english we use "to have". Like to have compassion or to have doubts.
I'm 90% sure that it was originally in the form of "to go <there/place> and <verb>" and has just been shortened over time. A refined colloquialism, if you go for that sort of thing