First, there needs to be some armor/shields/weapons that Allow you to gain extra heat/crowns/materials, or maybe make it a UV, possible like, Slime drop increase low- If you kill a slime type monster with that weapon you get slightly more crowns and a slightly better chance at getting a material from it. What do you think?
Next, is that I think that you should be able to test out unbound weapons that you say, got out of a box, in the training room, without binding it to your character, so you can see if you want to keep the weapon or armor, or sell it.
The last one is a new weapon, a one hit melee weapon, with a slow attack speed, no charge, high knock back, small hit radius, and [amazingly] high strength. Maybe a hammer or an axe?
I'm not sure about something to increase drops. Well, mats and heat probably wouldn't matter too much since they don't have THAT much value as it is, but more crowns is tricky because it potentially impacts on the cost of CE. Besides, give people a weapon or UV that gives them more crowns and virtually everyone will just go for that.
I believe the training test thing has been suggested (though more generalised in letting you test any weapon) and I'd love to be able to do that instead of putting down a lot of crowns and energy in the hope I'll be comfortable using something. Though I suppose the fact the current system makes people pay to test weapons means it's more profitable to not implement it.