For the most part, the number system actually reflects a pokémon’s registration to the International Pokédex, a vast index composed and maintained by a joint effort between the Pokémon League and the Pokémon Symposium. (You may know it better as the National Dex.)
However, it’s certainly not a perfect system, no, and it certainly gets complicated from there.
First, allow me to establish the cardinal rule of register pokémon to the National Dex: in order to register a pokémon with the National Dex, one must come up with definitive proof that a pokémon exists. In some cases, an evolution or a pre-evolution of a pokémon may be harder to obtain than the rest of the line, so the rest of the line ends up getting registered first, and the straggling member or members of the line are registered later, after the link is proven and established beyond a reasonable doubt.
Take the chansey line, for example. While everyone knew about the existence of chansey, blissey, and happiny, it was less understood how they were related. Chansey that breed on their own with compatible partners, without the aid of any external item, only produce more chansey. It was only within the past fifty years that it was discovered that giving the chansey that had gotten their hands on a luck incense before mating would produce a happiny, and only in the extremely recent past has this been done in a controlled environment to prove that a link between the two existed.
Blissey, meanwhile, was connected to the second, unwritten rule of registration to the National Dex: all of them followed a certain order. Putting it another way, the National Dex is the overall pokémon index, but every region has its own Regional Dex, consisting of pokémon either native to the area or that are known to be obtainable using methods best achieved in that region. So, while blissey had always been a known fact, for whatever reason, Kantonians have never been quite as skilled at achieving happiness-based evolutions as Johtonians, and thus, Kanto-raised chansey generally do not evolve into blissey. (Johtonians are, of course, completely unashamed of any comment they make towards Kantonians regarding this matter. Especially in light of everything else Kantonians say about us.) Thus, blissey is registered to Johto’s Regional Dex, but it is not registered to Kanto’s, despite the fact that its previous evolution is considered a Kantonian native.
Here is where the story gets a bit complicated. As I’ve mentioned a moment ago, Regional Dexes get indexed to the National Dex in a certain order, and that order depends on the establishment of the regional Pokémon League. The National Dex, after all, is a joint effort between the League and the Symposium, so without a League present, only a Regional Dex can be maintained for the sake of the scientific community. (Of course, we still know about the pokémon that live in each region. It would be rather preposterous to assume that we don’t. We simply can’t archive them in the official database that trainers rely upon, but they are indeed recognized by the scientific community regardless.) Once a League is established, the region’s own pokédex is added to the list, right where the National Dex left off. Thus, because the National Dex was originally established in Kanto, Kanto’s Regional Dex was archived first, followed closely by Johto’s because Johto shares many of its League resources with its sister region. Thus, blissey, despite being a known evolution of chansey, wound up being indexed over 100 places away from its predecessor.
As for why pokémon are numbered in the first place, it’s essentially for organizational purposes and for the sake of trainers. The pokédex, after all, comes in two modes. The first mode is the full pokédex, and the second is a notes mode, where all of the entries are blank. One of the unspoken duties trainers have is to assist the pokémon research community with their own observations (as battling and training are essential parts of a pokémon’s lifecycle that researchers, unfortunately, often cannot observe for themselves), and thus, the notes mode exists to allow trainers to record their own thoughts on their catches. Numbering each pokémon allows them to get a visual understanding of which pokémon they have and haven’t yet observed.
The Pokédex According to Bill 