Native English speakers, when you speak casually do you use standard pronunciation?

By “standard pronunciation” I mean you pronounce words exactly like how they’re designed to be pronounced (like “he” is a long /i:/ but “decide” is a short /i/, “clock” is a short /o/ but “saw” is a long /o:/, “food” is a long /u:/ but put is a short /u/, cats is pronounced with a /s/ but dogs is pronounced with a /z/...) Do you emphasize these difference when you speak casually?

In my school there is a subject called “speech training” that solely focus on making these difference stand out. Most of my classmates (and even I) agree that this subject is a nightmare. They complain that English speakers have these rules, but they may not take them so seriously as to focus on these differences every time they speak. My teacher explain that the differences are very important because if we don’t follow the rules, no native English speakers will understand.

So far I can pronounce words within the rules when I have to say one word at a time, but when I have to speak or read, I can’t seem to follow the rules exactly and I always pronounce some words the same way (like he and decide).