If you lined up 100 resulting images, 99 from weekend beginners and 1 from an actual artist. I guarantee you that you would pick out the artist every time.
It might be simple to trace over an image but you are probably better getting an artist to spend 2 hours on it, it will most likely look better than 2 weeks of tracing.
I think your art/design/craft is pretty good. Some people use pencils, some use Adobe products, you have gone out there and tried the new Dall-E medium.
Glad you thought out the usage, I am sure that when the novelty wears off that you will have that neat-as-octocat logo sorted out.
I appreciate that you appreciate the value that highly skilled designers bring to a product with their visual expertise.
However, I would like to see you A/B test the Dall E logo versus the winning designer logo. You could show odd IP addresses one logo and even addresses the other.
I think the designer would edge the robot for what you need (a logo), however, the proof is in the pudding and conversion rate.
People are already doing by combining DALL-E 2 with gfpgan for face restoration. So there may be a role in understanding how to combine these tools effectively.
As someone who is incredibly terrible at graphic design but knows what they like this could be a game changer as iterations of this technology progress. I can imagine going further than images and having AI/ML generate full HTML layouts in this iterative way where you start to define your vision for a website or app even and it spits out ideas/concepts that you can "lock" parts of it you like and let it regenerate the rest.
I'm not downplaying designers role at all, I'd still go to one of them for the final design but to be able to wireframe using words/phrases and take a good idea of what I want would be amazing, especially for freelance/side-projects.