LLMs don't have feelings, but they imitate humans who do. If your prompt sounds rude to a human, LLMs might respond like a human who is talked to rudely, if you don't want that, prompt politely.

Chatbots go through a reinforcement learning phase, which should be enough to make the LLM helpful regardless of the tone of the prompt, but you may still get better result if your prompt is made in a way that would get the most helpful response from a human.

It is not anthropomorphizing, it is helping the LLM recognize a pattern.

What if politeness is correlated to higher-quality answers in their mess of a "database"?

have you considered that when you stare into the void it stares back