> One can vote Bernie honestly but also approve of Hillary as a safety.

No, that's the thing. Many people want to express their preference, and really really didn't want to "approve" of these two people at the same level. It's exactly the same with...

> Bernie was quite popular and frankly a lot of people that also voted Trump also liked Bernie because he was an outsider.

...where these people may have felt positively about Bernie, but they really really preferred Trump, and they would not have "approved" of Bernie if that meant putting him at the same level as Trump.

So now you have two groups of people who would have preferred Bernie as their 2nd place choice, but decide not to "approve" him in order to help their 1st place choices win. Supporters of approval voting just keep ignoring this dynamic of how real people vote in the real world.

So I think your points are valid. I also just want to state that pretty much every cardinal voter I know prefers STAR then Score then Approval. I'm STAR 5, Score 5, approval 4 (only slight preference of STAR over Score). But I think that resolves your concerns. It is just that in practice we find that Approval is easier to argue for and is good enough. From a personal stand point I'll argue with technical people about voting systems if we got approval but I wouldn't be an evangelist anymore.

It's an iterated event, voters would learn that voting a single candidate generally gives them less influence.

Millions of Jill Stein voters would disagree with that.