Why am I repeatedly ask to "verify iCloud password"?

I have read the posts on this topic. What I don't understand is why Apple is doing this by email as opposed to requiring on-line verification the next time the user logs on to iCloud. When I first saw the notice on my iPhone, I thought it was fraudulent. I am very reluctant to put sensitive informaton in an email that, even with Apple, could be read by unauthorized persons before it gets to Apple.