And, how is it any more reasonable that you use, as a foundation, a treatise that was written well over one hundred and fifty to two hundred years ago for your interpretational foundation (Darwin, Lyell)? If recency of the material in question is all the rage, then why not throw out the old interpretational ring you seem to prefer?
Because new data to support it rolls in every day. We're not just talking about one old paper, or one old experiment - we're talking about a current, constantly-developing theory. Why replace it with, say, a bible that hasn't changed in over a thousand years? Darwin's book may be old but the thought in evolutionary theory is very new indeed - just like any other science.
So, do you have an alternate mechanism to explain the findings of radiometric dating?
I would point out that, since different, unrelated methods of radiometric dating tend to converge on roughly the same date (in situations where they could be expected to overlap), it seems reasonable to assume then that they're converging on the same date. Also, non-radiometic dating methods (varves, ice cores, dendrochronology) converge on the same dates as well.
What mechanism do you propose that would cause the same amount of error in all these unrelated, differing dating methods? That's really the heart of the matter - not what assumptions underlie any particular dating method, but why independant dating mechanisms converge on the same dates.