Why do solar planes have many small propellers instead of fewer large ones?
Because they are very lightweight and fragile. Therefore, thrust and propulsion mass must be distributed over span - a single, large propeller and motor would put too much force into the structure locally. Also, it would require a higher landing gear to give the larger propeller the required clearance.

You are right about the higher losses. However, these airplanes were built to reach record altitudes, and wing loading must be as small as possible to make that possible. Also, boundary layer problems on propellers are less severe than on wings because the rotation will cause the slowed boundary layer to be moved outwards from centrifugal forces. There the blade moves faster which will very effectively suppress flow separation.