Yes I have. the problem doesn't lie in the embedding though, as even when I open the image in Illustrator and edit it I get the issue.. You can see it less with photos like the one you have posted there, but if resize an image with lineart or text especially, or even the cut out of a person, you will start seeing some jagged edges here and there. If I resize directly in Photoshop the whole thing looks smoother.
I attached an example of what I am talking about. The edge of the card looks jagged even before it gets resized. Once it's sized down the text becomes jagged too. When I resized in Photoshop, the hard lines of the text (obviously the part that is in focus) remained crisp.
Sometimes clients might send me logos in raster format and they can't provide anything else (you know, JPG or PNG), and I found that the only way I could get around this issue was to stick everything in InDesign and resize there, or resize in Photoshop.
You may find that this is just how illustrator renders the raster image and when you actually output the artwork that the end result is as it should be. Here is a post on a similar issue: Placed high res bitmap in Illustrator not smooth, but jagged
I just did a test with a .png transparent background image and looked jagged on-screen but when I outputted it as a pdf it looked fine...?
I just think illustrator doesn't process raster very well..?
I hope some of this helps, sorry I can't do anymore.
someone in the post also states a good point that if you embed the artwotk it can then make it difficult to make any changes, etc.
This is because Unlike Photoshop, illustrator Don't "Resample" Image i.e Re-sampling involves Interpolation Techniques to Define Additional Pixels when an Image is Resized, common interpolation techniques are Bicubic (used by Photoshop), Linear etc.
Illustrator is Doing the Same work Photoshop do if we Uncheck the Resample checkbox in the Image Dialogue Box (at Image>Image Size) while Resizing.
Since illustrator doesn't implemented a Interpolation Technique, so it has to maintain Same Amount of Pixels, i.e If you Increase Dimensions, Resolution (PPI) will Decrease (and vice versa) to Compensate.
But why would it be creating extra pixels when we make the image smaller?
(Nop, while Reduction it Deletes some Pixels on Photoshop.)
Photoshop (while Resample is Checked) needs Additional Pixel for Enlargement and in case of Reduction it Deletes Pixels.
While Illustrator don't Add or Delete any Pixel, in fact it can't. (It could be a Feature Request to add Interpolation Technique in illustrator)
Illustrator can resample images.
You could use either the new crop feature or you could use the Object > Rasterize command.
I would not recommend either of them for production-ready resampling, because you still need decent sharpening after resampling.