It is one of outcomes of the assumption that two identical particles will obey the same physical laws. If all atoms of a particular isotope have the same decay probability now, we assume that identical atoms had the same decay probability a long time ago, too.
The other consideration is Occam's Razor. Constant decay rates are simpler, so we stick with that idea until we are faced with an experiment that is difficult to explain without variable decay rates.
There is nothing preventing science from adopting the variable decay rate hypothesis. All it takes is one good experiment.
RE: Why is atomic decay assumed to be constant?