Have you enabled at least one of the Destroy > By Quality options?

I believe how the Destroy > By Quality options work right now is: It destroys everything off that quallity.

Shouldn't there be a simple function that checks the price off an item (stack / nonstack) and give you the option to delete every item under certain value?

You can enable the By Quality options alongside the Below Price option for this effect. This way, items that are worth more than the set price will not be sold/destroyed, even if its quality option is checked under By Quality.

If you add items to an Inclusions list, then those items will be sold/destroyed regardless of the Below Price option.