Files with embedded profiles shown as untagged in Bridge.Bridge only right about files saved from PS

Question

Photoshop works perfectly when saving files as .psds etc. or PDF-Standards (PDF-X etc.), embedding the profiles correctly. However, InDesign and Illustrator do not embed any colour profiles in .pdfs, in their native formats (.indd and .ai) or any other format apart from .jpg.
Why is Photoshop working perfectly, yet AI and INDD are not? Everything was installed at the same time, and the colour management settings are all synchronised in bridge.
All I want to be able to do is save as one of the default PDF-X settings (via File > Save As in Illustrator), but as I said, saving as the same PDF-X standard across all 3 programs only embeds the profile if saved from Photoshop. I don’t have the slightest clue why Photshop is the only one that works.
Although, according to this post, which seems very similar to my question, it might be Adobe Brdige CS5 that is wrong: http://forums.adobe.com/message/3565578
Because I have files that Bridge shows as untagged, which upon opening do in fact have an embedded colour profile. Ugh, this stuff is confusing!

Answer 1

Thanks so much for your help, I didn't know any of those things. Very interesting.
In regards to Photoshop rasterizing PDFs, what exactly are the ramifications of that? A PDF-X saved from Photoshop is still fine to send to the print press, right?
So far, all the print work I do I design in the colour space specified by my printer, then save as a PDF-X1a (which is also what they specify), by doing 'Save As' in Illlustrator. I also name the file with the colour space, and my printer has not had any problems with this.
The reason I'm asking about colour management, is that I may start expanding into the area of designing adverts for newspapers and magazines, and this involves different colour spaces. And newspapers etc. around here won't be as fussy about colour management as my print-press, which is a very good print company. So it would be better if I knew they were getting PDFs from me with embedded colour profiles.
I think the situation is that when I save things with embedded profiles, that it does in fact work, despite what Bridge, Illustrator and InDesign say. I have .ai files that show up in Bridge as untagged, but when opened in Illustrator, do indeed have an embedded colour profile.
It's very confusing to know what's going on.
A rather non-technical workaround, which alot of people seem to use, is just designing the file in the correct colour space, saving the file in that colour space, naming the file with that colour space, and then when it gets to the printer/magazine/newspaper etc. hoping that (A) there is colour profile data in the file that people can see at the destination or (B) the people at the destination know from the file name that you designed it in the correct space, and so they just Assign Profile at their end, and all is well.
I mean, what's the alternative, I can't suddenly stop using Illustrator and InDesign, and doing ALL my work in Photoshop, just because of what Bridge says!