Granted that we have, say, 3 hours of office time per week (required at my institution), is it acceptable to set per-student limits on usage of that time, such as: 20 minutes per student per day?
In order to evaluate this situation, I think it is worth starting with the "Devil's advocate" argument for why it might be okay for one student to take up all the time. One could reasonably make the argument that, so long as there are no other students waiting, the allocated consultation hours might as well be available to the one student who wants to use them. (Obviously if other students are being crowded out then an equity issue arises, and in this case it is reasonable to limit student time so that everyone gets some consultation time.) If the university requires a given number of hours to be made available for consultation then it is an institutional requirement for these to be available to students. While this may be tiring for the lecturer, if that is a job requirement, it is arguably a situation where the tiredness of the lecturer is irrelevant. Refusing to allow consultation in those hours to the only student who wants to be there is arguably a breach of the university's requirements for consultation time. Finally, the argument that there is an "equity" issue involved when only one student seeks to make use of an offered resource is weak --- if no-one else wants to use that resource then there is no inequity in him using the whole thing.
I think the above is roughly what would be a good argument in favour of the student here. But notice that even under this view, this does not mean that the student should have carte blanche to have the lecturer give them anything they want within the consultation hours. Consultation hours certainly should not be used to redeliver lectures and tutorials for a student who has not absorbed those sessions. It is reasonable to impose some structure on the consultation sessions and some requirements on student effort in order to ensure that those sessions actually advance the goal of student learning (as opposed to creating a perverse incentive for lack of effort in lectures and tutorials). The suggestion to confine consultation to help with problems on which the student can show a preliminary attempt/effort is perfectly reasonable, and it ensures that there is some focus to the session. It is also reasonable if the lecturer responds to these cases by giving further hints or suggestions for the student to go away and re-attempt the problem, rather than giving a long and detailed solution. (The latter may be required after several attempts, but it need not be a first response.) For more general inquiries about concepts, etc., one could again require preliminary student effort by having the student gread the relevant material and give their own explanation of the concept in order to get your feedback; you can then point out flaws in their reasoning and have them re-read the relevant material and come back to get more feedback later.
Even if one accepts the above argument that a student may legitimately use all the consultation hours, one can easily turn this stamina-competition around on the student --- this merely requires that the structure of the consultation assistance requires preliminary student work and the feedback on the work is quicker than the preliminary work required to gain that feedback. For example, if each preliminary attempt at a homework problem takes 10 minutes, and the lecturer feedback giving hints/suggestions on the problem then takes 2 minutes, then the student will need to spend five times as much time working as the lecturer. In this case the student will be the one who has to spend large amounts of time working and getting physically tired, and this is likely to yield a natural limitation to the monopolisation of consultation time.
Additionally, is it advisable to be forthright and tell the student that their behavior is unusual/a bad sign/an abuse of the office hours; that is, that they should be mostly responsible for the material on their own?
Monopolisation of consultation time is arguably not an abuse at all, so I wouldn't suggest taking this line. Similarly, telling the student they are mostly responsible for learning on their own ---when you are actually supposed to be offering consulation in this time--- is arguably contradicatory to the university's consultation requirements. However, use of excessive consultation time is often a warning sign of failure to learn the material properly in lectures and tutorials, and it is perfectly reasonable to be forthright about this.
If the student has no capacity to follow along in class, read the book, or make connections on their own (as you describe) then this is the core issue. If this is the case then it is reasonable to give the student feedback pointing out these deficiencies. In some cases it might be that a student lacks sufficient preliminary knowledge/skills for the course, in which case you could direct them to bridging courses and resources (e.g., study-skills center at the university, etc.). Alternatively, if they are close enough that the problem is fixable in the present session, then it might be worth "stepping back" to look at the meta-problem --- if they are not able to follow along without one-on-one consultation then perhaps the best use of consultation time is to try to assist them to develop this capacity, rather than spoon-feeding them with help on particular course problems.
