After discussion, allowing a few pre-defined classes and adding table to the whitelist would capture most of the value of full styleable tables (though in the long term styling would be good, either as an extension of this editor or in our own editor).
Classes should give the ability to create something akin to this and this (preferably including both optional sorting and colored backgrounds with a decent collection of available colors), as well as handling simple infoboxes and image containers (a border and slightly tinted background is fine).