Hashing only works if the website stores their passwords correctly. If a single website you use doesn't hash passwords correctly, and gets their database leaked, then your passwords will all be leaked. Changing a few characters per site may help a bit, but it shouldn't be relied on.
Also, if you're worried about the host shutting down, you should try bitwarden. It's completely open source, and you can self host it if you want.
Corporations are neither evil nor nice. They are indifferent. By design they only care about money, they don't care about anything else.