The final cost for assembling a receiver with a power cord is higher than one without. One reason it's detached is that it's easy to automate the line that packs the box and if a robotic line inserts on in each box, there's no reason to worry about someone taking a break and having a series of boxes with no power cord, so no labor cost is associated with it and the line can run all day, every day.
As far as the cord being adequate, a lot of times, 'just' needs to go before 'adequate'.