It's a pretty well known problem in the generative image domain. GPT-image-1 (and gpt-image-1.5) are outliers in their ability to generate images with a proper alpha channel.
You can still use other models (Flux, SDXL, NB, etc), you'll just need to request that the image be generated on a solid colored blackground. Then just run it through Rembg [1] or similar background removal tool.
[1] - https://github.com/danielgatis/rembg
