There are two ways to read your questions:
1. Would we be better off never feeling negative emotions because they were never called for--i.e., because we never experienced the sorts of events that make grief or anger an appropriate reaction? Or...
2. Would we be better off never feeling negative emotions regardless of what happens to us?
I am inclined to answer 'no' to the second question. While some (e.g., Stoics and Buddhists, at least on an oversimplified reading) suggest that we should approach negative events with a level of detachment that make grief, anger, or despair inappropriate, and the wise or enlightened person will reach a point where she can avoid feeling such emotions, I find that approach inappropriate. I think it would be both mistaken and almost inhuman not to feel grief at the death of one's child or not to feel some level of anger at the terrorists who perpetrated 9/11 (whether despair is ever appropriate is trickier). So, I do not think we would be better off if we could get ourselves to stop feeling these emotions no matter what happens to us. There's another question here, which is whether we could have been built such that the appropriate response to tragic events was not negative emotions, but if that were the case, I'm more inclined to say we would not really be human anymore (notice the Stoic or Buddhist is not built so as to never feel these emotions; he has to develop that attitude).
The first interpretation of your question suggests the debate about the problem of evil and suffering. It seems like an all-good, all-powerful God could have made this world a 'heaven on earth' such that we could be built the way we are but we simply did not face any (or many) tragic events. Then we could be human and still avoid any (or as much) despair, grief, anger, and suffering. Wouldn't that be the best of all possible worlds? Well, answers vary here. Some think tragic events and our appropriate emotional responses to them are necessary for us to become better people, build virtues like courage, and learn to empathize (of course, without tragedy, the need for courage and empathy is minimized). When I teach the problem of evil, I like to point out that without tragedies and the negative emotions that go with them, we'd certainly have less interesting literature and movies. But I have to say, I don't think this whimsical point nor the 'soul-building' defense are strong enough to explain why an all-good God would allow so much suffering (especially so much suffering of innocent children).
Here's a riddle your question raises too: If God exists and is entirely perfect, does he (can he) feel any negative emotions, such as grief and anger? If so, how? If not, then it would suggest we'd be more perfect if we were less human and more godly.