There are several situations, where graphics should be compressed with options, unavailable in Photoshop at all.
As I said before, Photoshop does not allow you to change
Chroma subsampling method when saving JPEGs. In simple words, it leads to lower resolution of color channel comparing to lightness channel.
For high resolution photographic images (originals), it doesn't really matter, because there are no single-pixel details. But when you have to deal with reduced images, single pixel details can be easily found there, and compressing it with 4:2:2 subsampling (default and unchangeable setting in Photoshop) obviously leads to averaging of color and degradation of detail level.
Same thing applies to situation, when you have color text annotations or any graphic figures (arrows, leader lines ...) in JPEG image. If these objects don't have antialiased edges and/or lines are quite thin (1-2 pixels) it makes really nasty compression artifacts. To avoid it when using Photoshop, you have to use low compression level (close to 100%). But if you have control over the chroma subsampling, compression can be set to reasonable level.
Sometimes, you can achieve better visual quality with higher compression (same or smaller size) by using 4:4:4 subsampling mode.
So, problem with Photoshop is not in inability to compress graphics (it can do it somehow), but in very limited compression options, leading to quality degradation you can't avoid without other tools.
In addition, I can mention lack of control over image metadata - you can have EXIF/IPTC, but Photoshop will rewrite it, or you can ditch everything when using Save for Web...
Using Photoshop, you can't compress to desired size (let it automatically pick required quality to fit into size restrictions of forums, online forms, applications and so on).
Speaking of image resampling (shrinking) - Photoshop stopped its evolution about ten years ago. There are several useful resampling methods, available in other software. Here is some sort of
visual comparison - samples are arranged by local contrast, produced by different methods after shrinking original image three times. I also have
numeric evaluation of these methods.