As an employer in the biomedical research area, I'm interested in searching for some people with a background or interest in chemistry or life science application development. Since this is a software development-centric site, it's likely that job seekers won't include this kind of information in their primary tags, even if they are interested in the field. But, I think it's the kind of thing that people might end up putting in their personal statement. I realize personal statements are going to be really noisy, but it'd still be nice to be able to dig, IMO.
I have some chemistry background (my degree program was originally in Chemistry before I saw the light and switched to CSc), but I wouldn't ever think to mention it in my personal statement -- you'd only see it show up in my early work experience and in some safety certifications.
So the best way to find me (if you're looking for a programmer with some chemistry knowledge) is to be able to search through all the text in my resume, not just a specific part. So IMHO, such a search should be configurable to search in any subset of sections.
Maybe it would help too if employers could create tags and if there was a tags page with stats. In SO/SF/SU/Meta, the tags page shows how many questions are tagged with a certain tag. Here, tags could show the number of CV's that use that tag in likes, favorites, and experience to employers, and the number of searches that have been done using a certain tag to employees.
This would allow an employee to choose tags that are searched that describe him and he would not have thought of. Yes, there is a chance that some optimize their CV according to search stats, but that cannot be prevented (as most buzzwords are known even without stats).
I do agree with the OP though that all fields should be searchable (including the personal statement). This should not be a biggie, as the trilogy sites implement full text search too.