Well, there's some degree of such a problem, but in general they aren't such a big deal.
Think of it this way: if a sentence can have two different meanings based on different Hanja (Chinese characters), then they will be ambiguous when spoken. Obviously, a language cannot function if a lot of sentences are ambiguous. Therefore, when ambiguities arise, native speakers invariably figure out some way of suppressing the ambiguity. (A commonly confused word may lose its position to another similar word with distinct sound. An additional word (say, an auxiliary verb) may be used to disambiguate the context, and given enough time, may even become a grammatical suffix. Or people may just decide "what the hell" and just borrow an English word.)
For example, your example of "I bought a cha" might normally be expressed like this in modern colloquial Korean:
나 차 좀 샀어.
na cha jom sasseo.
I bought a little cha.
(This clearly implies "tea": how would you buy a little "car"?)
나 새 차 샀어.
na sae cha sasseo.
I bought a new cha (= car).
(This is somewhat hard to explain, but it implies that the speaker bought something brand new. It would be a rather odd expression to use on teabags.)
Or even more idiomatically:
나 새 차 뽑았어.
na sae cha ppobasseo.
I "picked up" a new car.
(The verb "ppop-da", literally "to pick up", is a colloquial expression for buying something expensive or worth bragging about.)
In fact, English itself is quite prone to ambiguity (although at a different level): famously, "time flies like an arrow" can be parsed in at least five different ways. Although this is a made-up example, I've seen many English learners struggle to understand complex sentences in, say, New York Times, because pretty much every English word can be a verb or a noun at the same time. Of course, all these sentences are perfectly clear to a native English speaker.
Thanks for fleshing it out. I'd add also that context is often set (in any language) outside of a single example sentence. So a word, or sentence in isolation can be ambiguous, but in the context of a conversation or a book or whatever can be pretty clear.
Ambiguity can be great as well, lots of poetry, clever puns and jokes rely on ambiguity of specific words to add multiple layers of meaning.
Well, there's some degree of such a problem, but in general they aren't such a big deal.
Think of it this way: if a sentence can have two different meanings based on different Hanja (Chinese characters), then they will be ambiguous when spoken. Obviously, a language cannot function if a lot of sentences are ambiguous. Therefore, when ambiguities arise, native speakers invariably figure out some way of suppressing the ambiguity. (A commonly confused word may lose its position to another similar word with distinct sound. An additional word (say, an auxiliary verb) may be used to disambiguate the context, and given enough time, may even become a grammatical suffix. Or people may just decide "what the hell" and just borrow an English word.)
For example, your example of "I bought a cha" might normally be expressed like this in modern colloquial Korean:
나 차 좀 샀어. na cha jom sasseo. I bought a little cha. (This clearly implies "tea": how would you buy a little "car"?)
나 새 차 샀어. na sae cha sasseo. I bought a new cha (= car). (This is somewhat hard to explain, but it implies that the speaker bought something brand new. It would be a rather odd expression to use on teabags.)
Or even more idiomatically: 나 새 차 뽑았어. na sae cha ppobasseo. I "picked up" a new car. (The verb "ppop-da", literally "to pick up", is a colloquial expression for buying something expensive or worth bragging about.)
In fact, English itself is quite prone to ambiguity (although at a different level): famously, "time flies like an arrow" can be parsed in at least five different ways. Although this is a made-up example, I've seen many English learners struggle to understand complex sentences in, say, New York Times, because pretty much every English word can be a verb or a noun at the same time. Of course, all these sentences are perfectly clear to a native English speaker.