It's important to understand the technological limitations here. In theory, IP addresses are globally unique and assigned through a hierarchy of non-profits, with IANA at the root. So, in theory, if IANA wanted to prevent North Korea from having IP addresses, they could do that (they don't actually want this, as explained in other answers). In practice, it's a lot messier.
Each internet service provider (ISP) peers with other neighboring ISPs, and with Content Delivery Networks (CDNs). This means that they agree to exchange traffic at one or more fixed Internet Exchange Points (IXP). An IXP is, basically, a bunch of switches, which both ISPs or CDNs connect to in order to exchange traffic. But that's just the physical hardware. There's another piece to this, the Border Gateway Protocol (BGP).
An Autonomous System (AS) is an ISP, CDN, or other large network (e.g. Google) which is responsible for administering its own IP addresses. BGP is the "language" that AS's use to tell each other* things like "I know how to reach IP range X, so send all its traffic my way." In theory, each AS is responsible for filtering these instructions to only include the routes that "make sense." Otherwise, for example, an AS might erroneously or maliciously claim to own "All of the internet" (or some appreciable subset thereof), and send traffic in the wrong direction. Unfortunately, that actually happens on a fairly regular basis, see for example this recent incident, or this list of older incidents. It's a serious problem, but not the subject of this question.
My point is that BGP is a distributed protocol. There is no central authority with the technical ability to unilaterally control which IP addresses are routed where. Instead, each AS decides which IPs it will route internally, and which IPs it will route to another AS. If, for example, a North Korean AS and a Chinese AS agreed to route some block of ostensibly Chinese IP addresses into the North Korean AS, there is nothing anyone could do about it. In fact, this behavior would likely be invisible to most of the internet, unless you happen to operate an AS that peers with North Korea, or have some reason to suspect a particular connected device of being in North Korea and not China. But North Korea need not peer with anyone other than Chinese ISPs, and internet access is heavily restricted in North Korea, so this could be effectively kept secret.
In short: At a technical level, IANA doesn't try to restrict IP addresses in part because doing so is impractical at best and wholly ineffective at worst.
* BGP can also be used within an AS, called Internal BGP. We're mostly not talking about that use case, but you should be aware that routing information is needed throughout any large network, not just at the edges. IBGP is one way of distributing that information, but not the only one.