Pokemon Home definitely needs some more details. From what I can tell, Pokemon Home allows you to transfer Pokemon one-way from PokeBank, Pokemon GO and Let's Go Eevee and Let's Go Pikachu to Pokemon Home but you can both send and receive Pokemon to and from Pokemon Sword and Shield with Pokemon Home.
In other words, it sounds like a separate PokeBank-like app for the Nintendo Switch, meaning that Pokemon Home will likely require a separate subscription. As for why you might want to have keep your PokeBank subscription, it sounds like you won't be able to transfer Pokemon from the DS and 3DS family to the Pokemon Switch games without having both.
As for why it might only be one-way from PokeBank, the only idea that comes to mind is that Pokemon Sword and Shield change the formula in such a significant way that older generation Pokemon need to first be changed via transfer to Pokemon Home before they can be sent to Pokemon Sword and Shield.
Welp, at least this confirms that we'll be able to keep transferring our Pokemon to the new generations as they come out, just means that PokeBank subscriptions costs have essentially doubled (if not more because of Pokemon Home's trade functionality). But again, we need more details before we come make any concrete conclusions, perhaps we'll get them during next week's Pokemon Direct.
Edit: Here's the image for people who didn't see it: