reviewing the zygarde pmd lore posts i was brainstorming on here a few years ago,
the "voice of life" refers to multiple entities who watch over parts of the pokémon world. this includes hydreigon of course, but also other characters that have been the ones to send humans to the pokémon world (such as gardevoir). voices of life are often mythical or legendary pokémon but can be other kinds of pokémon for various reasons (for example, it's not like hydreigon has to split its duties like a legendary pokémon does). celebi is an example of a mythical voice of life, but it's only a voice of life in the future (and also thanks to time travel complications the version of celebi that summoned takahiro also died. but that's kind of neither here nor there)
anyways, the voices of life act largely autonomously from each other. the goal of a given voice of life is to maintain balance at all costs, and their ultimate boss is zygarde. whose goal is also to maintain balance at all costs.
the reason why voices of life tend to throw humans at their problems is because it makes for a human-pokémon pair that could never otherwise exist in the world, which fulfils a certain want for balance.
but all the same in order to maintain the balance of the otherwise humanless pokémon world, they make the humans take the form of pokémon. previously the humans would have also had to go back to the human world to maintain balance as well until kellen's wish for tenma to remain in the pokémon world (gti poststory) which rewrote everything for everyone following tenma. which is also why space distortions start happening but are also, like, mostly fine.
zygarde cells also probably play into this in some form as well. or something. ^-^