In other words, did Shakespeare ever write of 'going to the hospital?' Or did George Washington ever write that a soldier must 'go to hospital?'
Dropping the article in front of other seems like a stereotypical fake Russian accent. In American English, believers 'go to church' or 'go to temple.' When and where did these exceptions for the use of a definite article before certain, apparently 'special' objects of the preposition arise? When and where did they fall?
This is not a historical development, as such. Though nor is it usage which may be explained with a hard and fast rule, as there is some dialectal variation with respect to it.
What we are observing, essentially, is that English nouns require an article where they are countable, singular and concrete (“I found a quarter”, but not “I found quarter”) and do not require an article where they are abstract and uncountable (“the boy has spirit” is acceptable), or countable and plural (“the boy has legs” is acceptable).
But the prior category can give way to the latter in particular in cases where what is otherwise or previously a count noun is treated in an abstract fashion which construes it as uncountable. The extreme case of this is word such as “heaven” or “hell” which for conceptual reasons, cannot be enumerated in a given cultural context. One goes “to heaven” rather than “to the heaven”, as to qualify which heaven one is referring to, or how many, would be nonsensical (in a majority of English Christian contexts), making a countable use of the word impossible, and the interpretation of the word as uncountable the natural development. And indeed, in a less extreme case, when we say we go “to church”, we are implying our attending the uncountable abstraction of the church concept, rather than a specific edifice which is therefore countable. Though in this case, both approaches coexist, as they often do. Which nouns conventionally see this usage or these changes in countability is, however, as I say, subject to dialectal variation.
Thanks to Google Ngrams, you can see this historical development for yourself. Here for British usage. Here for American. And here for all books written in English worldwide.
Saying "going to hospital" arose in British usage around 1850, becoming more popular between 1920 and 1960. It has declined since then. It never became a thing in the US. Why some British writers started using this in 1850 is a point for an historical linguist.
In other words, did Shakespeare ever write of 'going to the hospital?' Or did George Washington ever write that a soldier must 'go to hospital?'
Shakespeare never wrote "the hospital". Washington never wrote just "hospital".