Learn English – How to distinguish formal words from informal words

No, therefore should not be reserved for conclusions beyond a reasonable doubt. It is merely a transition similar to thus or as such:

Therefore, I ordered pepperoni.

Thus, I ordered pepperoni.

As such, I ordered pepperoni.

The extended conversation could have been:

I like meat on my pizza. Therefore, I ordered pepperoni.

You can test for an appropriate use of therefore by flipping the sentence order and using because:

I ordered pepperoni because I like meat on my pizza.

The contention that the therefore segment should be restricted to perfect logical use is forgetting that the word really only serves to draw a causal link between statements.

I like red. Therefore, I painted my wall red.

There is no logic here. I am just explaining why I painted the wall red.

Now, if someone is using therefore as a logical link and the logic sucks, you can say that the argument is bad. But the use of therefore isn't the problem.

This $10 item is 50% off; therefore I am saving $6.

This is wrong, but the use of therefore isn't incorrect because it is simply communicating the thought. The communication is accurate; that makes therefore the appropriate word. Replacing therefore with a different word changes the meaning of the sentence (and could correct the logic) but the intent of the speaker no longer matches the communication.

Edit: Since there seems to be some confusion about the actual definition of the word, here is what my dictionary says:

for that reason; consequently : he was injured and therefore unable to play.

Reason, in this context does not mean "logic". It just means "why".

Why couldn't he play? / He was injured.

He was injured and therefore unable to play.

He was unable to play because he was injured.

It is worth noting that there is a strict logical use for the term therefore that explicitly means something akin to "logically derived from the previous statements" but that would be applicable to formations of the following:

1. All men are mortal

2. Aristotle is a man

3. Therefore, Aristotle is mortal

This is commonly represented by three dots in a triangle (∴). But even in this case, the use of therefore is a signal of a specific meaning. If the conclusion is false, it was not an incorrect use of therefore but simply faulty logic. Removing or changing the word doesn't make the problem go away.

As an American, I can report that everyone I know, even highly educated people, use these forms several times a day. People in business meetings, professors giving lectures,... everyone. Sometimes people are being slow, clear, and deliberate, in which case they will pronounce the full phrase, which does sound more formal by comparison.

My sense, as an amateur linguist, is that the problem lies on the fact that it is difficult to quickly turn the vocal cords on and off. (Please note that "gotta" is actually pronounced /g'ɒdə/, with a d sound) It takes time to slow down and make the change. In each of these examples, the entire word is pronounced with voiced sounds. These types of drifts happen in every language and lose stigma over time.