You can run some image models locally if you want to prove to yourself how well they can do with just a single generation from a prompt with no extra steps.
I've done this enough to suspect that most hosted image models don't increase their running costs to try and get better results through additional passes without letting the user know what they are doing.
Many of the LLM-driven models do implement a form of prompt rewriting though (since effectively prompting image models is really hard) - some notes on how DALL-E 3 did that here: https://simonwillison.net/2023/Oct/26/add-a-walrus/
I've done this enough to suspect that most hosted image models don't increase their running costs to try and get better results through additional passes without letting the user know what they are doing.
Many of the LLM-driven models do implement a form of prompt rewriting though (since effectively prompting image models is really hard) - some notes on how DALL-E 3 did that here: https://simonwillison.net/2023/Oct/26/add-a-walrus/