On most medium to large projects specs are provided. If not I may require them if there is information I need that should be in a specification. On most, the spec books are between 1,000 and 2,000 pages. I identify and book mark the information I think I will need, usually before I start looking at the plans, then do it again as I review the plans. For most of the information I think I need to determine code compliance, if it is in the specs but not on the plans I simply make note of it. Sometimes, a violation occurs in the field that prompts my re-involvement where the contractor or inspector says the info wasn't on the plan. I point them to the spec book, which typically neither entity has seen. I often find inconsistencies between the specs and the plans.
However, some information I do request to be on the plans. Doors and hardware are an example of this. I always check the specs, and review them for code and plan consistency, and will make comments that point to the specs in that case. Occasionally I get resistance when I ask for information to be duplicated on the plans. My response is that if they really don't want to, I can't make them, but that when the inspector needs to verify something and can't because nobody on sight has access to, or is willing to look through a 1,000 page book to find the answer, the job may be delayed until someone finds the information. So far, in every case the DP provides the information, even if it is just pasting the spec pages onto a blank page. It only takes them a few seconds nowadays.
For most things, I let the specs stand, but for issues I think will cause that type of situation I encourage some information to be put on the plans.
In my entire career I can't recall any inspector, or the contractor that is on site for the inspection having access to the specs in the field. A few times I might see them in the job trailer, covered in dust. And even if the specs were available, having the time or inclination to leaf through them is a luxury not available to most. So I try to make it easy on everyone by trying to get the information they need to succeed in their hands as easily as possible. I have never met continued resistance when I explain that.
Now, getting anyone to look at the plans....whole 'nother story.