We show that if comets (or any small icy planetesimals such as Kuiper belt objects) are composed of pebble piles, their internal radiogenic as well as geochemical heating results in considerably different evolutionary outcomes compared to similar past studies. We utilize a 1D thermo-physical evolution code, modified to include state-of-the-art empirical measurements of pebble thermal conductivity and compression, the latter obtained through a new laboratory experiment presented here for the first time. Results indicate that due to the low pebble thermal conductivity, the peak temperatures attained during evolution are much higher than in any previous study given the same formation time. Assuming meteoritic radiogenic abundances, we find that only extremely small, sub-kilometre comets have the potential to retain the primordial, uniform and thermally unprocessed composition from which they formed. Comets with radii in excess of about 20 km are typically swept by rapid and energetically powerful aqueous hydration reactions. Across the full range of comet sizes and formation times, evolutions result in the processing and differentiation of various volatile species, and a radially heterogeneous nucleus stucture. Our computations however also indicate that the assumed fraction of radionuclides is a pivotal free parameter, because isotopic analyses of the only available cometary samples suggest that no 26 Al was ever present in comet 81P/Wild 2. We show that if comets formed early in the protoplanetary disc (within 1-3 Myr), the radionuclide abundances indeed must be much smaller than those typically assumed based on meteoritic samples. We discuss the importance of our findings for the formation, present-day attributes and future research of comets.