There are a number of great reasons why it makes sense to build your room design on and around the rug.

The rug is literally the foundation of the room. It supports everything, including the occupants.

It's likely the most expensive item in the room

It's also likely to be the most enduring item in the room. A well cared-for rug can last centuries. Matching a slipcover to the rug is a lot less expensive than matching a rug to a slipcover.

It's wonderful inspiration for the colors in the room.

It determines the genre of the room.

It  is the most scarce of the room's furnishings.  Within our own building there are 750 rugs but 85000 fabric samples. Paint choices are infinite.
Don't get boxed in with limitless products forcing a second or third choice on the most precious of furnishings.