It's all but certain that there's something wrong with the shardblades. They're ridiculously awesome, but they seem to be antithetical to some in-world notion of Honor (with a capital H since that's the name of one of the gods). Hopefully we'll get some more explanation in the next book, especially since we'll see two people with windrunner powers (Kaladin and Szeth), but only one has a shardblade (and it's the one whose life seems to have been forced down an evil path, which might not be a coincidence). I think Dalinar giving up his shardblade will have positive consequences for him as well.

For Shallan, I'm not certain about this, but I think she keeps the shardblade a secret because she only obtained it by killing her own father (possibly in self-defense or in defense of a family member). The family didn't even know he had a shardblade, but it would have appeared when he died, and she took it. It would be understandable that she wouldn't want to tell anyone about it, even if it would solve their money problems.

I'm desperately hoping that Words of Radiance is better than Steelheart or A Memory of Light, both of which I found largely uninspiring. I hope that more Stormlight is just the thing to get him back on track.