Hi Team,
No, it's not possible to add labels to image fields in the rich text field. This is not something that will be re-implemented as it goes against the recommended workflow of using Slices described here.
What will happen is that we will properly deprecate it by removing labels from being selectable when an image is highlighted as this causes confusion and gives the impression that labels can be applied, though as you’ve seen they cannot.
The recommended way of creating a page layout such as this is using slices. This works even better with Slices labels.
Another slightly different way to model your content like this is to have different slices for different text presentation.
For example, you would have:
1x [Full-width text block] 1 x [Text and image block with Slice label to set image alignment]
Then with these 2 Slices, you can build dynamic pages easily, like so:
[Full-width text block]
[Text and image right]
[Full-width text block]
[Text and image left]
Let me know if this makes sense or if you need a more solid example.
Thanks,
Phil.