Upon reaching the daily vote limit, I see that first posts and late answers reviews are grayed out. Since voting is not the only thing I can do on reviewing those, why is this so?
I found a question on Meta StackExchange from 2012 that is asking about the same thing. You can find it here:
There was exactly one answer to this question which I will copy for future reference on this site (emphasis from original author):
I think it is because the First Posts and Late Answers Review tasks not only allow you to make necessary edits as you see fit, but also upvote and downvote questions or answers which you wouldn't be able to do if you have reached your vote limit. You would not be able to effectively review those queues as a result.
Low Quality Posts, Suggested Edits and Close Votes on the other hand, do not require or allow upvoting or downvoting on posts, thus it is still available on your Review tasks.
All in all you can't do everything you would normally be able to do when reviewing these queues once you reached your daily upvote limit. Because of this it's only natural to disable this queue for you so that every review from you has the same capabilities and especially to ensure that every review of first posts or late answers can be made by someone who can vote on them.
Personally I think it's important to upvote a new users post if it's good to give them their first reputation, allow them access to some basic privileges like posting on Meta and because I feel that the queue is to give new users feedback on their behaviour on the site. This is equally important as giving them feedback on how to improve their posts by posting comments and pointing them to important resources like the Tour and the Help Center.
You can still keep an eye out for things like "answered x minutes ago by xyz 1/101" on the homepage. Users with 1 or 101 are very often new users or relatively new users on the site or StackExchange in general. You can still comment on their posts and give them feedback on how to improve or where to find stuff. But you should leave the review, which is intended to give reviewers the chance to vote on the reviewed post, to those people who can still vote on any given day. They have all the tools available that StackExchange deems important for this kind of review, while you don't have them available for the rest of the day.