Halacha=not strict enough?

Hi!

I am basically undergoing a shiur (orthodox) in Germany.

I am attending most of the classes from our Rebbe and i noticed some inconsistencies.

For example: A processed product [food] can only be kosher if the ingredients are kosher, the animal is kosher and technically a rabbi is attending/checking the process.

However my rabbi argued like this: If you buy milk (from a cow obviously) [in a german grocery store], you dont need to check if it has a kosher certification (which anyways barely exists in germany lol). Because germany has high standards in food production, a jew [in germany] can assume the animal was kosher (like non injured) and the process of milk production didnt involve other non kosher steps or contamination. So the milk can be consumed.

My question now: Basically anyone in germany knows that most of the cows [in intensive live stock farming] are indeed injured or sick to a certain degree. Even though the processing of the milk kills basically all bacteria etc. the milk shouldnt not be considered kosher because the producing animal is not.

Why are this kind of simplification allowed in countries that dont have this kind of developed kosher manufacturing (like israel or USA) even though they are halachically forbidden?

Thank you!