If any of the assumptions I stated were taken individually, sure, you could still say that this specific assumption, by itself, cannot account for the apparent age of the sample,
but all the assumptions are in effect in every age determination.
And I notice you had no comment on why different radiometric dating methods (uranium-lead, lead-lead, potassium-argon) often produce wildly varying ages on the same sample, resulting in a guess based on the index fossils (assumed to be of a certain age) located near the sample.
I agree that it is possible for contamination of a single sample to produce ambiguous results from differnet differential tests. I'd like to know the metrics and evidence to support the assertion that this "often" happens. A handful of anecdotal cases out of hundreds of thousands of sample analysis readings does not constitute "often".
but all the assumptions are in effect in every age determination.
The assumptions are consistent with the observed physical properties of the radioisotopes. The calculated time spans are based on observed decay rates. An assumption of a maximum age of 6,000 years requires an assumption of a decay rate that has never been observed.