Yes fasts and thermals generally have varying cross sections. The graph of fission products don't vary much. The "well known" ability to identify which reactor a used rod came from, is because the fission products themselves react to neutron flux, and for materials science reasons no one runs rods to more than a couple percent burnup and long enough to stabilize.
So a rod isn't just 1% used up (a vacuum?) and 99% pure and unused, its first hour of fission at a certain rate resulted in a certain random distribution of nuclei which themselves were irradiated for precisely 2345 hours of full power operation, and then hour two's fission products got irradiated for 2344 hours, repeat. Its a massive summation. What makes it even more complicated is some of the product nuclei are themselves radioactive with a pretty short half life (this is where the ten or so percent of decay heat energy comes from ...) so if you shut it down from hours 1023 to hour 1025 then the end result product will be quite a bit different because you're missing two hours of product isotopes, missing two hours of irradiation for the old isotopes, and the old isotopes decayed naturally for two hours (perhaps into different isotopes, some of which might be radioactive).
If you're really bored, and want to run a big numerical simulation, and have programmatic access to a nuclei table (or just make one up with random data?) you can have all kinds of fun simulating a reactor and summing, decaying, and reacting hundreds to thousands of isotopes under varying conditions and then seeing what you get.
Maybe a TLDR is there are a lot of ways to properly ignite charcoal for a charcoal grill, but the end result cooked steak tastes about the same in the end.
So a rod isn't just 1% used up (a vacuum?) and 99% pure and unused, its first hour of fission at a certain rate resulted in a certain random distribution of nuclei which themselves were irradiated for precisely 2345 hours of full power operation, and then hour two's fission products got irradiated for 2344 hours, repeat. Its a massive summation. What makes it even more complicated is some of the product nuclei are themselves radioactive with a pretty short half life (this is where the ten or so percent of decay heat energy comes from ...) so if you shut it down from hours 1023 to hour 1025 then the end result product will be quite a bit different because you're missing two hours of product isotopes, missing two hours of irradiation for the old isotopes, and the old isotopes decayed naturally for two hours (perhaps into different isotopes, some of which might be radioactive).
If you're really bored, and want to run a big numerical simulation, and have programmatic access to a nuclei table (or just make one up with random data?) you can have all kinds of fun simulating a reactor and summing, decaying, and reacting hundreds to thousands of isotopes under varying conditions and then seeing what you get.
Maybe a TLDR is there are a lot of ways to properly ignite charcoal for a charcoal grill, but the end result cooked steak tastes about the same in the end.