Supply voltage requirement of MAX1190x is shown below: One reason why there is a narrow supply voltage range may be because the power supply rejection ratio of this device is not very high. In addition, since it is designed for low power applications, low supply voltage is crucial.
A screen capture of the Electrical Characteristics table showing power supply rejection of MAX11902 (Rev 1 4/15) is shown below. It is relatively simple to add an LDO such as MAX1725, which comes in 5pin-SOT23 package. In most precision systems, powering an ADC with its own LDO regulator can improve system performance.