Why not reach the foot of the rainbow?

You never reach the horizon, nor can you fly to the rainbow feet. That's because both cases need a long distance between the object and the new observer to create the effect.

Source: cisl.ucar

The rainbow actually consists of many drops of water absorbing light in some way. Round, clear water droplets refract and reflect a few rays of light to the observer. Light has different wavelengths refracted at different angles, so the white light of the sun is separated into a range of multicolored light.

Because these brilliant scenes are made up of light and water, don't expect to find its stop. This optical phenomenon depends on whether you have to stand away from water droplets, and the sun must be behind your back.