You would also need to change the entire ecosystem: if you use standard mattresses, then you can leverage the existing supply of sheets etc. Which is not to say it's a bad idea, but I imagine there's much more involved.
You could sell the custom sized mattress at cost, but then charge a premium for the sheets. That way you make money off of the sheets, which wear out more quickly than a mattress anyways.
Patent the square sheet form factor and you can lock out competitors and/or get hefty licensing fees. (as well as method and application of turning a sheet 90 degrees to hide coffee spots under pillows that you will then license at no cost to buyers of your brand of sheets while suing buyers of competitor's sheets)
