I need help with science. thanks?
It isn't exactly about assuming that decay rates are a statistical constant, it is that the processes which make decay happen are basic to the universe itself and do not change with time (no secular variation in the laws of the universe), so decay rates, in bulk over time, are essentially constant. We can use that presumption to employ radioactivity for a number of purposes, but it is only important in the sense that the purpose would not be valid if the behavior was not constant. We would have to find some other useful applications for radioactivity.
We assume that the rate of radioactive decay remains constant.That means that the proportion of various isotopes of elements is relative to various events. With carbon dating, for example, the relative proportions of carbon 12 and carbon 14 depend on when the object being tested died. There are several other examples over many time scales.
Because without that assumption (and thank you for admitting that it is JUST an assumption), everything based on it falls apart completely. Also, please do not confuse uniformity in nature with uniformitarianism. They are not the same. The former is an observation that the laws of physics and balances of nature work across the world and universe. The latter is an assumption that the rates of change we see today are themselves unchanging.
Uniformitarianism is an assumption that physical laws are consistent over time. It's probably true and it's what we base most of science on but we can't be absolutely 100% sure (because there is no way to test for it). One of the reasons why it is important in the case of radioactive decay, is that we use that to measure how old things are and for that to be accurate or meaningful we need to assume that physical properties are consistent over time (i.e. it's our best guess until we figure out some other way to do it even more accurately to double-check).