My personal opinion about why Shallan and co. didn't sell the Shardblade is that it's far too risky. It's not like there's just a black market for Shards sitting around, and even if they just bee-lined it straight to the King of Jah Keved and offered him the Shardblade, there would be many eyebrows raised. House Davar is described as of middling importance - ancient, yes, but not very powerful or influential. The King would probably not buy their story of "We have no idea how our father got this Shardblade, but please buy it so that we can save ourselves from debt," even though it's the truth. There's just too many ways that he could think of how Old Man Davar got the blade, all of them suspicious (assassinating a Shardbearer, theft, etc.). I also can't imagine that such a deal, even if it were to go through, could remain secret for that long. It would attract a huge amount of attention to the Davar house, which is exactly the opposite of what they need (an argument could be made that with the ludicrous amount of money made from selling the Shardblade, the Davars could simply bribe people to keep them quiet). If someone discovered that they also had a Soulcaster, they would probably get fried for heresy, and all the risk of selling the Shardblade would be for nothing.
Is stealing from Jasnah a better idea? Probably not; it's still insanely risky and there are about a million ways it could go wrong. However, if Shallan was able to pull it off, she would be able to create those mineral deposits that made their family rich in the first place, give it to the Ghostbloods, and essentially kill two birds with one stone. If she simply sold the Blade, she would have nothing to combat the Ghostbloods with except bribes (which probably wouldn't work).
I'm not trying to disprove anyone's theories or ideas; this is just my own opinion on why Shallan decided to not sell the Shardblade. Now that I think about it, your theory works a whole lot better, Gloom. Ah well, this is all just an idea of mine.
As for the Soulcaster: it states in the book that Shallan's father's soulcaster had been sheared in two places: "across one of the chains and through the settings that held one of the stones." (p. 502) Since Shardblades (presumably) cut through the Spiritual Realm, it would make perfect sense that the Soulcaster was damaged so that the trapped spren or whatever powers it was released or damaged. Probably stating the obvious here.
Also, if Shallan did kill her father with an ordinary weapon, how did the Soulcaster get cut with the Shardblade? Or did she immediately take the Shardblade after he died and start hacking at him with it?