In general, LEDs are quite replaceable, although ignorant clerks may tell you otherwise.
This might be true for some lights, but for my particular sewing machine, replacing the LED would require disassembly and soldering. It's not as easy as simply unscrewing a bulb and putting a new one in. The labor costs alone would me more than what I originally paid for the machine, which is why the technician told me to just buy a new one.