I don't know about other countries but yeah it happens here sometimes in the U.S.
This may not be true for everyone, it depends on the speaker and it usually only happens when someone is speaking fast. They probably don't even notice it. If Kid Cudi were to say that sentence slower, then he'd probably pronounce the "t."
I never notice these things until someone points them out. However, I did notice that this omission of the "t" usually depends on the order of the words. If an American (or at least most) was to say "why must I," you would definitely hear the "t" that helps to make the "st" sound. In this case, the t is right before "sh," which would make some people drop the "t" and go straight to the "sh." You'll also notice this in the way some Americans pronounce "sentence." Some of use say "senTence" other say "seNence."
Just a little note, in songs, people tend to distort words because it gives the song more appeal. I was just listening to a few songs and I thought to myself "Wow, if a non-native speaker used these songs to practice pronunciation...they would sound really weird!" It happens in pop songs, rock songs, rap songs, etc. Just be aware of that. Thanks for the song, by the way.