Who said anything about making a profit? If Google could make Bard work as well as GPT-4 they would do it, even if it had to operate at a significant loss to start.
It's a stunt now for both companies as it's a proxy for both search, AI capabilities for sale, and clouds. But eventually they will reach a limit of payoff. But 4 months is short for product development, especially as it sounds like google was caught off guard by the public interest in interacting with chatgpt.