Some of this flexibility is already suggested in the game, it just needs to be expanded on.
There’s already a table recipe in the craft menu (craft menu - not construction menu) and all you need are more options for the recipe. You can then place the table from the construction menu.
We just need more placeable furniture that can be crafted and transported as regular items beforehand. This approach would provide more options and flexibility than the rigid construction menu and allow you to bang all your furniture into cargo carriers if you want to move it great distances (or loot a house for furniture if you’re lazy).
It still bothers me a little that someone took away the “place anvil” construction too, that’s hinting at the wrong direction to take regarding furniture, though isn’t really an issue in itself.
edit: though we’ll need interactions with more furniture to “pick it up” or “take it down” like you do with tourist tables, funnels etc.