Is it always bad to use "get" or "got"?

Wow! The admonition "don't use got" has gotten a lot broader than I remember it being. When I was young, what overly-picky grammarians complained about was using "got" (or "have got") to mean "possess" rather than "acquire" or "become". This seems to have been a feature of colloquial American speech for quite a while

I've got a mule; her name is Sal.

15 miles on the Erie Canal.

(song from 1905) but it has often been regarded as an incorrect usage in American English.

Because of this, the grammar police now seem to discourage all uses of the word "get". There was a children's book I read to my daughter when she was young where the copy-editor seems to have replaced "wouldn't you like to get one" with "wouldn't you like to have one", which would be fine except (1) that particular use of the word "get" was perfectly correct and (2) the line no longer rhymed with "pet one".

I would recommend (a) not using "got" to mean "possess" in formal speech and (b) otherwise ignoring the grammar police.

Short Answer: No, "get" is not always bad.

Longer Answer: "get" and its derivatives have many meanings and uses.

The first example you give "I got broke" is not considered standard, but it's what lots of people say (that is, if your lawyer uses it, it'd be pretty weird unless your lawyer was from the deep South and they were talking about a kettle and not some law).

So it is an acceptable past passive in certain dialects/registers ('good ol' boy' talk), but not mainstream.

"I got a ticket." is mainstream, but not as formal sounding as "I bought a ticket."

Otherwise, 'get' for received, is certainly very standard and respectable.

Just for perspective, I have heard that in British English, 'gotten' actually sounds a bit more formal than 'got'.

The word "got" means received or suffered. In your examples, your suggested alternatives means different things entirely.

"I have a ticket" and "I purchased a ticket" do not mean the same thing as "I got a ticket". If you always had the ticket it, you have it now. But you didn't get it. If you "got a ticket", that means you received one.

If your arm "was broken" then you can't have broken it because it was already broken. If your arm "got broke", that means you suffered a break to your arm.

I don't see how any of your examples are ambiguous. The only issue is "got broke" should be "got broken". For example, "In the car accident, the driver's arm got broken."