Note: It seems that this change was a bug; see this answer. While my answer below is not really valid, we can still expect that this change will happen eventually, and when it does the logic presented here will still be just as valid, so I am leaving it here.
The new reputation levels are the standard levels on graduated sites. Previously, we had the public beta levels, for which close votes were available at 500 rep (and, for instance, Trusted User at 4k). If you go to any other graduated site, the rep levels will be essentially the same (barring individual changes).
This site has been ready to graduate for a while though, and formally did so in September. The biggest immediate consequences of graduation are moderator elections and removing the "beta" label. After some time, the rep levels will also be raised (as it seems they have) and a custom site design will be added. This is part of the new design-independent graduation procedure which we are one of the first sites graduating through.
I can't comment on why it took so long for the rep levels to be raised, but this was always understood to be part of the graduation process, and is not in any way unexpected.
Personally, I'm all for this change. We want to encourage more people to continue participating for longer on this site. Having rewards at higher levels serves this purpose. Previously, for many users on the site, once they passed 4k rep, there was nothing else obvious to aim for. Now we have things that even the highest rep users can still aim for. The new levels are still rather reasonable; it's completely possible to get to 3k in a couple months if you're relatively active.
From a practical standpoint we can easily still deal with close/reopen voting and other reviewing whether there are 42 users or 162 qualified; a question only needs 5 close votes, and 42 is pretty large compared to 5 already. In addition, this site has been around for some time and has some rather well-established policies on closure. We want the people who are voting to close/reopen questions to at least be aware of these rules before voting. A user with 500 rep could plausibly not know any of these rules, as getting to that level only takes a few days of activity at minimum. A user with 3k rep will likely have been around for a while and probably at least knows enough to intelligently decide on these things. Sure, some users in the 500-3k range are qualified and know the rules, but even with just 3k users there's not going to be much difficulty getting things reviewed. At worst, it may take an extra few hours to get questions closed or reopened. The only front that we're lacking people on is answer deletion, and that's a rather rare case anyway.
With that said, I would like to remind and encourage everyone here to be voting on posts. If you read a good question or answer, upvote it. This is the best way to ensure that people here can maintain healthy reputation growth. In addition, I encourage everyone to ask good questions yourselves. There's been some complaints recently that good questions to answer are increasingly hard to find. However, few have taken the obvious step to counteract this of simply asking your own good questions. You can even answer your own question if you prefer. If you follow these steps, I expect you'll find that these rep levels are actually still within reach in a reasonable period of time.