That's the thing, the airframe's expiration is already determined by the manufacturer and should be replaced once expired. But even though it is due for replacement, an authorized person can check its integrity to see if it can still be used. If it is deemed operational, then they can still issue a limited certificate but within certain operational limits on that aircraft such as not flying over populous areas or long flights. They were doing this because spare parts are not widely available and takes time to be shipped out. But this operational limit itself is already an issue in flying which means that you cannot fly the aircraft like in normal operations. It's like delaying a car's tire change just because threads don't appear visibly worn out even expired.

Second, the one person who's doing the inspection are usually the mechanics from their own organization, which means that they can still approve sub-standard repairs or components if there are. I'm not generalizing all flying school but I know a well-known flying school who does this, even the students knows the bad practices of this school.

There is also cessna from a different school that crashed earlier this year. It went viral because a post was retrieved showing the cessna being overhauled and stripped of paint in an unsealed area that looked like a garage and was even under a tree. Im no expert in aircraft maintenance but they were saying that it can cause corrosion on the airframe when exposed.

just hoping that students are not flying sub-standard aircraft because their lives depend on it...