If you are going to go through the effort of building a PBN, you should probably make sure it lasts for as long as possible (hopefully indefinitely).
And if you want it to last for as long as possible, then you want to make it harder to identify the fact that it is a link network.
One way you can help hide it is to host the sites at different IP addresses. There are also many other steps you probably want to take to hide the fact that it is a link network. Think about all the different ways that someone could identify whether your sites were connected somehow. These are called footprints. You want to minimize your footprints and blur them as much as possible to make the network harder to identify. Spreading your sites across different IP addresses is just one way to help do that. But there are many other things you need to do also besides that if you want it to be hard to detect.
One of the most overlooked footprints in a link network is the structure of the network's outbound links. It is also a common footprint found in homepage backlink networks that makes them incredibly easy to identify. When you have a handful of websites that all only link out to the same other websites, it is a really easy pattern to identify. That is an easy pattern for Google to spot. In order to blur that footprint you should make sure your PBN sites link out to useful pages on popular authority sites so that each site's outbound linking pattern is diluted and mostly unique (except for your links to your money site). You lose some of the link juice by linking out to other authority sites, but you increase the likelihood of the link being trusted by Google.
If your PBN is a tiny one like just a handful of sites, then you can be a little less careful about hiding things. For example, if you were building just 3 private sites to create 3 private links under your control, you should be able to get away with it just fine by having them all on one IP. If you were going to do that though, then there is also no need to hide anything. Just make the sites useful sites that you openly declare your ownership of. Google won't really care if you do that. It's okay if you interlink your own sites in reasonably small numbers. What they care about is when you create significant numbers of links (or substantially powerful links) just for the purpose of manipulating your rankings or for manipulating PageRank.
If you intend to build out a large PBN and push a huge amount of link juice then it becomes much more important to blur footprints. With each new site you add to your PBN, it becomes increasingly more important to hide footprints.