Like the other commenter said, these models aren't trained against images with an alpha channel. Given the same sized model that'd make typical results worse to benefit a niche case. You should be able to have them generate this style image on a background you can color key out though.

Those examples look nice and would be trivial to automatically cut out/trace into transparent vector with inkscape

That's because it was trained on RGB images without an alpha channel. There is currently no public image generator that understands alpha channel.

As a user, this really frustrates me. Promoting is not precise enough to compose a bunch of specific elements, so the obvious solution is to do several prompts each with transparency and then combine in Photoshop/photopea. I end up asking for a white background and then cutting out manually

I feel like someone could satisfy this issue with a little background removal AI in the pipeline. I also go through the same process, stitching together a few tools, and obviously it's possible... but it sure would be nice if it all fit together better. Something where "transparent background" was translated to "white background" or something and then it went through the background removal.

The closest I've found is vector generative AI like what's in Adobe Illustrator today.

Luckily there is another AI for removing the background (:

Thankfully, MacOS and iOS have a fantastic ML powered "extract the image content in to a new image with transparent background" function that you could use on this silly output to get what you want.