Yes, it's definitely by-design.
The following tools are available to you when reviewing first posts from the review queue:
- Voting up/down
- Voting to close (on questions) or delete (on negatively-scored answers)
All of these except for editing are rate-limited in some way. And of the five, voting and editing are the two most important - not only are they critical to the overall quality of the site, but specifically in the case of new users, they are our primary means of welcoming new users and demonstrating our commitment to high-quality questions and answers.
So if you can't vote, you're left with editing as your primary tool in this queue. While I'd love to think this was enough, in practice folks vote a lot more than they edit - even on Stack Overflow, there are only 2 people consistently averaging more than 30 edits a day. Editing takes more time and effort than any other action on that list, hence the lack of external rate-limiting. If you're diligently editing all or most of the posts you review, more power to you - and if you're done for the day in the First Posts queue, you might find your skills put to good use by either the Low Quality or Suggested Edits queues.
I find editing/close votes/comments to be a better tool personally
Close votes are also rate-limited, can only be used on questions, and even then only used on a minority of questions. If you have close votes to burn, there's a whole queue waiting for you... Comments are nice, but also the most toothless of the bunch - and they also suffer from the same problem as editing: leaving good comments takes more time than anything else. If those were the only tools available to you, it would be a pretty useless queue.
Voting is the easiest, fastest, and IMHO most useful thing you can do in the First Posts queue - if you do nothing else, please vote. And if you burn through all of your votes reviewing first posts, consider that the sign of a job well done. Thank you!