The difference is due to qualities of text training data used in training the two types of model.
The LLM models are trained on large amounts of text, and learn grammar rules very well. There are lots of examples of negation in the training data. The trained models can process what negation means in phrases, and what that may mean for the following phrases, i.e. what they are likely to generate when a term such as "no elephants" is in the previous context.
The image models are trained on images paired with image descriptions. Part of the image training process involves creating a shared multimodal "concept space" where text and image descriptions both resolve to the same descriptive vector*. This allows the generator to measure how far away a generation so far is from an image with the same description as its text input. It can then use that to adjust the image pixels towards something with a more similar concept vector to the text.
The thing that is generally missing from the image/text pairs is negation. It is rare to have images described by what is not in them, and definitely not text generally covering all the details in a complex image - like your zoo image - that are not there. There are therefore very few places in the "concept space" which cover the negation of some element or other. In fact you often get the opposite effect in a generator like DALL.E - the more you mention an element, positively or negatively, the more prominently it will appear in the image.
Image generators can and do allow for this. They allow the use of negative prompts (Stable Diffusion), or prompt weights which can be negative (Midjourney). These work by adding the negation of the concept vector, based on the text in the separate negative prompt. The image, whilst generating, will be adjusted to not be like, or not contain, the concept in the negative prompt.
I don't know why DALL.E does not support the use of negative prompts.
* It's more complex than that, what I describe is very roughly how CLIP guidance works.