I do see what you're saying. However this debate isn't unique to this specific scenario. The exact same reasoning can be applied to other violations of due process. Historically that was viewed as a particularly dangerous slippery slope and thus we have the concept of fruit of the poisonous tree, despite that this can easily result in (for example) a mob boss walking free. Perhaps caution is warranted when considering abandoning well established principles?

https://en.m.wikipedia.org/wiki/Fruit_of_the_poisonous_tree