My guess is that it is done to prevent the player from diplomatically vassalizing all small countries in the last stages of a WC. In most cases you need more than 5k autonomy modified dev to be able to vassalize a 100 dev country even if the limit would not exist.
I think that is a niche reason. I doubt Paradox wants to gimp a WC playthrough if they already made it so far.
Is there any historical example in which such a big country accepted to become a vassal without at least the threat of war? (in eu4 you have to be allied to the target, so it can't apply to situations in which the country is afraid to get killed).
First, in EU4, the whole alliance requirement is gameplay only. It's just ahistorical. I think we all agree with this.
But if I were to give examples, one of the most famous is Ptolemaic Egypt. The Romans took Egypt without war. There's a lot of drama but essentially the last ruler willed it away to the Romans. In fact, the Romans threatened many nations into unfair alliances, which then turned many into client states. I argue that alliances does not necessarily mean it's strategically beneficial for both sides. Some nations were forced into an alliance. It's a join me or die attitude. If you go back even further, majority of the Persian satrapies had a similar choice.
One can also argue that "vassal" is a very loose term. There were many vassals that had a wide variety of control from their overlords. Some were essentially independent but branded nominally as a vassal. In that case, many examples fall under that category without needing an alliance, further proving that if you are big enough, you can strong-arm nations to be your underling. The type of underling just depends on historical context.
I don't think that you can argue in this way, because if this would apply, a country should immediately surrender unconditionally if they are attacked by a vastly stronger country.
I want to note that no one implied "immediately" here either. So you can't change my point like that. Sometimes, it takes one battle to realize the war is lost. That did happen a lot. Shu Han of the Three Kingdoms essentially gave up against Wei after a brief invasion. The Mongols were another example. A lot of minor European wars were essentially a few battles and capitulation.