"Factory Man" actually addresses these questions in considerable detail. You might be surprised how difficult it is to produce good-looking finishes, veneers, etc -- especially at scale. There was a time when the American manufacturers thought their competition would never catch up (and then they explicitly trained their competition so they could outsource production, which backfired when retailers realized they could cut out the middleman and order directly from China/Vietnam/wherever the cheap labor currently is.)

American furniture manufacturing does have one significant advantage in the US compared to its offshore competitors: proximity. Furniture is bulky to store and time-consuming to ship. The one manufacturer who realized this, John Basset, is the titular "Factory Man" who has kept his factories running by doubling down on just-in-time delivery, etc.