Pokémon Home lets players trade Pokémon between games, including the ones on different platforms. This should theoretically allow fans to keep their entire Pokédex from Pokémon Ruby and Sapphire onward, as Pokémon from Gen 3 can be brought forward to the Gen 6/Gen 7 games, through the use of Pokémon Bank on Nintendo 3DS, and sent over to the Pokémon Home app. Pokémon Home has yet to be compatible with a new Pokémon game at launch and there are a few reasons why this is the case.
Pokémon Home launched in February 2020, which meant it was available after Pokémon GO, Pokémon Sword and Shield, and the Pokémon Let's Go games were already released. The app managed to be compatible with the Pokémon Sword and Shield Expansion Pass at launch, but that involved a game that was already available. As of the time of writing, Pokémon Home isn't compatible with Pokémon Brilliant Diamond and Shining Pearl or Pokémon Legends: Arceus.
Pokémon BDSP still lacks Pokémon Home support, even though they launched nearly six months ago. It might seem as if Pokémon Home might not be important to The Pokémon Company, even though it's a paid service, but there's more to it than that. There are technical issues standing in the way of having Pokémon Home available for new Pokémon games at launch, and there is also a design choice that could be involved, as having Pokémon Home available at launch would potentially dilute the core experience of the series.
Why Pokémon Home Support Is Missing From Games At Launch
The simplest explanation for why the new Pokémon games don't have Pokémon Home support at launch is that it's a lower priority than getting the games themselves out on time. The fact that Pokémon Sword and Shield and Pokémon BDSP had lots of glitches at launch proves that developers were down to the wire with getting the games ready, and there wasn't enough time to fully test them. Unlike the bug-riddled days of Pokémon Red and Blue, the new Pokémon games can be patched, so it's not such a big deal if there are game-breaking bugs, as they can quickly be fixed via an update. Once the Pokémon games are fixed and the online infrastructure is implemented/bug-tested, then Pokémon Home compatibility becomes the priority.
A more generous explanation is that the developers simply want players to engage with the game in the way that they envisioned at launch. If players had access to their entire Pokédex dating back from Pokémon Ruby and Sapphire, then they would have the chance to craft the perfect team ahead of time and would steamroll through content. Part of the magic of Pokémon (and why Pokémon Nuzlocke runs are so popular) is the feeling of exploration and forming a team of Pokémon that are found in the wild.
The Pokémon games prevent the player from using high-level Pokémon too early, through the use of the badge system, but simply having a team of six well-balanced Pokémon with good stats at the start of the game would make everything considerably easier, even if they were low-level. If the new Pokémon games lack Pokémon Home support for the first few months of launch, then players are forced to engage with the games as fresh new trainers with a single starter. Pokémon Home is a great concept, but having access to it during the launch window of a new Pokémon game would make it easier to break the games than it already is.