I agree that an accent can be attractive to people and can be an asset for you. However, I disagree that Schwarzenegger's accent has always been an asset for him. While it has generally worked for him in roles like Conan and the Terminator, I would say it was a liability in his now-defunct political career. Countless standup comedians have mocked him over the years for the ponderous thickness of his accent.
Look at the other end of the spectrum, at someone like Zsa Zsa Gabor, who clearly showed that she was quick and smart and sophisticated while retaining the "spiciness" of her Hungarian accent. Same with Ivana Trump. And Sofia Vergara has a very amusing accent on Modern Family (though she gets criticized for making it too stereotypical). And American politicians often play up their dialects as well; JFK and Bill Clinton come to mind.
So it can definitely be an asset.
I don't know if you can get a real answer for a question like this, but I think it's good to keep this in mind: A little goes a long way. I think the best course of action is to master English as best you can, with as little accent as possible. Through mastery, you will begin to understand which parts of your accent are good to keep and which should be removed. I think it's important to show that your accent doesn't impede your quick understanding of English in any way. You don't want your accent ever to get in the way of actual communication, so mastery of English is crucial.
And it's not like you will forget how to speak your original tongue. You can always re-assess and change how much of it you want to incorporate into your English. I suspect this is a process that evolves over a lifetime.