I know for example in Japanese, instead of saying 私はライアンです (I'm Ryan) it becomes ライアンです "(I'm) Ryan" as that sounds natural, it's like if saying "I've traveling to the US." which simply in Japanese becomes イギリスに旅行に来ました. Basically it's rewritten as "(I'm) traveling to the UK". (This nuance often gets mistranslated via anime or JP media).
In this case by saying アメリカに旅行に来ました [There's no 私は in this sentence] is akin to saying "Traveling to the US" when omitting I'm entirely, so you have to infer "who" which in this case is the PERSON IN FRONT OF YOU or TEXTING OR CALLING, so you've established who you are talking to based on presence of mind and situational awareness.
You need to use own brain to infer based on context rather than being direct (as in Japanese), if the speaker says "Who are you talking about" when omitting "I'm" or "We" or any other proverb entirely, you refer to yourself by stating amongst the lines of "You're talking to me, right?" to convey to the speaker that you're are the person they are referring to.
For example, if saying お腹が痛い "~~(My)~~ stomach hurts" [It's not: 私はお腹が痛い] as YOU or the [PERSON] in question is the subject, so there is no need for 私は (I am / my) but if they said 誰？(Who?) then simply state 私です (Me.) to clarify afterward. But saying 私 alone sounds robotic, that's how they would know you're using Google Translate.
Try reading this sentence (with subject omission akin to Japanese - absence of pronouns such as I'm, we, us, we're, and so on, The result below is what it would like if it was written in the Japanese format:
財布をカバンから出し、好すきな子の為に高い宝石の支払いをした。
Took wallet out of bag and paid for expensive jewelry for the girl whom liked.
It's definitely not written as:
彼は彼の財布を彼のカバンから出し、彼は彼の好すきな子の為に高い宝石の支払をした。
Seeing 彼 5 times in one sentence drives me insane and annoying to read, as there is no point, so in Japanese they omit it entirely, you HAVE to INFER on context. (The sentence: 財布をカバンから出だし、好すきな子の為に高い宝石の支払いをした from Japanese feels more natural to read without saying 彼 over again.)
The complete sentence (pronouns ommitted - conveyed in brackets) from Japanese:
(I) took (my) wallet out of (my) bag and paid for expensive jewelry for the girl whom (I) liked.
This is one of the reasons why a language like Japanese gets "lost" in translation, for example in manga or anime subs, as there is no 私 or 僕 in every sentence the same way as it is in "Western" languages, from their eyes it is considered "Vague" if they are not aware of Japanese grammar.
It does pose issues for inexperienced translators from JP > EN as they find it hard to distinguish on who to pinpoint since they do not use "I am" in the same way as English, since Japanese is a "pro-drop" language, in which pronouns or possessives are omitted, as they expect the audience to infer based on context.
I mean, can you still understand it if you OMIT the subject or pronoun to the same extent as Japanese, but in English sentences? Like this one:
went to Times square to meet up with a friend who lives here, such a good (pal).
Grammar is only done by design in the realms of Tokkien, Martin, or Star Trek. For naturally occurring ones, the spoken language comes first, then the grammar in an effort to standardize it. So a design flaw in grammar is bit of an oxymoron for me.
Cultural norms have an influence on grammar. About 400 years ago people in England still distinguished between a familiar you (thou) and a polite you (you). And over time decided to be polite only and only retained the thous and the thees in archaic expressions. And caused the need to disambiguate the plural from the singular you with new pronouns. Japanese grammar tends to get longer the more polite and humble you want to speak. So I don't think your can divide culture from grammar neatly. Both of them make the hypothetical exchange I made up 5x as long.