So the consensus seems to be that the classic UNIX line-based tools match the regex against the line excluding the newline terminator (which makes sense since it isn't part of the content of that line) and therefore $ only needs to match the end of the string.
If you read a line, you usually remove the newline at the end but you could also keep it as Python does. If you remove the newline, then a line can never contain a newline, the case cat\n can never occur. If you keep the newline, there will be exactly one newline as the last character and you arguably want cat$ to match cat\n because that newline is the end of the line but not part of the content. It makes perfect sense that $ matches at the end of the string or before a newline as the last character as it will do the right thing whether or not you strip the newline.
If you want cat$ to not match cat\n, then you are obviously not dealing with lines, you have a string with a newline at the end but you consider this newline part of the content instead of terminating the line. But ^ and $ are made for lines, so they do not work as expected. I also get what people are complaining about, if you are not in multi-line and have a proper line with at most one newline at the end, then it will behave exactly as if you are in multi-line which raises the question why you would have those two modes to begin with. Not multi-line only behaves differently if you have additional newlines or one newline not at the end, that is if you do not have a proper line, so why should $ still behave as if you were dealing with a line?
If you read a line, you usually remove the newline at the end but you could also keep it as Python does. If you remove the newline, then a line can never contain a newline, the case cat\n can never occur. If you keep the newline, there will be exactly one newline as the last character and you arguably want cat$ to match cat\n because that newline is the end of the line but not part of the content. It makes perfect sense that $ matches at the end of the string or before a newline as the last character as it will do the right thing whether or not you strip the newline.
If you want cat$ to not match cat\n, then you are obviously not dealing with lines, you have a string with a newline at the end but you consider this newline part of the content instead of terminating the line. But ^ and $ are made for lines, so they do not work as expected. I also get what people are complaining about, if you are not in multi-line and have a proper line with at most one newline at the end, then it will behave exactly as if you are in multi-line which raises the question why you would have those two modes to begin with. Not multi-line only behaves differently if you have additional newlines or one newline not at the end, that is if you do not have a proper line, so why should $ still behave as if you were dealing with a line?