There is no incentive for a manufacturer of products whose RF frequencies are illegal in Europe to include a power supply that works on European voltages. It's not specifically that the European products work on a wider or different band WIDTH, but that the work on different frequencies because different frequencies are used for different things in Europe and the US.

The power supply is just a dumb transformer, diodes, capacitor and regulator. No voltage switches. No auto input voltage switching. If you get a US travel adaptor, you will then have a string of stuff coming out of the wall, but it should work for you.