Why does capitalization exist?

Yes, I agree with Vincent B. In European languages, if I should generalize, capitalization is used to allow easy parsing, be it sentence onsets, nominals (esp. in German with a complex clause structure), or just proper nouns and in some cases honorary pronouns.

I do not know the history behind capitalisation, but I can tell you about some practical uses I've found in my experience.

Mainly, it allows me to see when a new sentence starts. I find that full stops are difficult to see (especially in handwriting) because they are so small, so I often go by the capitalisation instead.

On top of that, it allows me to recognise proper nouns in cases that I'd otherwise mistake them for common nouns. This is useful with words like "Rose", where the common noun refers to a flower and the proper noun refers to a person.

Some languages add rules. For example, German extend this capitalisation to all nouns. As legatrix pointed out in the comments, this is rather useful to language learners as it can help them guess sentence structure much easier. However, as krenkz says in his answer regarding Czech, this can get confusing even to native spreakers when too many rules are added.

Since you mentioned computer systems, it's worth mentioning conventions in programming. Capitalisation is useful for recognising macros or environment variables. Also in variable naming, capital letters separate words without spaces, for example likeThis.*

I doubt this is why capitalisation started to exist. My uneducated guess is that some scribe just thought it looked pretty. However, the reason it still exists in modern English and in most Greek-derived alphabets is because it does have practical value, especially in handwriting.

*Yes, snake_case exists, but I think it's ugly, and I don't see it being used outside Python.

I do not have enough reputation to comment and I do not have an answer - because I do not believe that there is a simple answer to any of your questions. So just some comments to why do we care about capitalization in real life?

My native Czech is a prescriptive language with complex capitalization rules: apart from marking a sentence onset, they are used to mark proper nouns and boy, these rules are something - not only do you have to know sometimes very particular logic concerning a small group of instances, but also the history of their usage, e.g.

• if a geographical proper name consists of 2 adjectives + 1 noun, you must write the first adjective capitalized
• a question arises what to do with the middle adjective and the rule says: if there historically existed or still exists a synonymous name with only 1 adj + 1 noun, the middle adj. must be capitalized, e.g. Medvědí jezero –⁠ Velké Medvědí jezero (Great Bear Lake), Západní Karpaty –⁠ Vnější Západní Karpaty ("External" Western Carpathian Mountains)
• if the 2-word name did/does not exist, the middle adjective stays with small letter, e.g. Severní ledový oceán (Northern "Icy" Ocean), Velký bariérový útes (Great Barrier Reef)
• notice that the noun will follow its own rules to decide whether it will be capitalized or not.

And this is just one example. The thing is that younger generation of Czech linguists started a discussion whether The Czech Academy of Science should not stop prescribing these rules and move towards description (also because capitalization does not play any role in the spoken form and children spend really a lot of time learning language rules and even then - obviously - in reality people make plenty of mistakes - I mean, the Academy provides a service answering via email curious questions from the citizens and capitalization rules cover the overwhelming majority of these questions). Still, if you ask laymen, literally everybody will be against abolition (or just relaxation) of these rules. It just does not make sense - I consider it akin linguistic Stockholm syndrome.

Btw I remember a local linguistics conference where a speaker argued for the relaxation of these rules, giving examples of their absurdity, all linguists approvingly nodding their heads - to spend the following two hours passionately arguing about the capitalization in those examples given in the speech.