The laws of Kashrut are quite complex. In fact some things might technically be okay even Halachically but women/men have been stringent and this became the custom.
In regard to your question although one could in theory clean a pot and wait 24 hours so that there is no unkosher taste (it becomes פגום). This is Rabbinically prohibited for fear one might accidentally not wait the appropriate time. In addition perhaps one cooks a sharp food that rejuvenates the taste. Similarly Nullifying is not straightforward, first of all it should not be done intentionally ש׳׳ע יורה דעה צט, סע׳ ה.(ie: used as a loophole only as a leniency if done accidentally). See ש׳׳ך יורה דעה, צט, ס"ק ז who says it is rabbinically prohibited - though some others hold it is prohibited by the Torah.
And so going back to the example of a clean pot cooked after 24 hours, if it was deliberate. Pri Megadim (M.Z. OC 451:2) penalizes him and forbids him to eat the food. Igros Moshe (YD 2:41) disagrees, and although it is forbidden to do this there is no penalty and the food may be eaten.
Similarly it might become very difficult to determine how much of the permitted food is necessary to nullify the pot. For instance when only a kzayis (olive) of milk was used in a clean pot, then it can be nullified with 60x a kazayis. However if you regularly use the pot for milk the day before (without knowledge of the amount) then the whole pot must be nullified see יורה דעה צח:ד. Now if that milk pot had a some meat cooked in it, the pot is now prohibited (due to absorbing milk and meat). No longer can it be nullified against 60x the meat, but instead must be nullified against the 60x the milk and meat, which in this case is the pot once again. This last part is a disagreement see יורה דעה צח:ו and also the ט׳׳ז there. So although 60x can cause nullification it is not always so straightforward and simple.
So it is Rabbinically prohibited so that you not accidentally not clean the pot (mixing actually food stuff), or in case you don't wait the appropriate time (mixing taste), and that intentional nullification of a prohibition is not allowed. Finally even if all these issues were moot, it is not straightforward to nullify things and a Rabbi should be consulted.