Tropes can absolutely be based in reality. A trope is simply a commonly used stylistic device or convention in media. Sometimes it's commonly used because reality just works that way. There nothing inherently cheap about it.

Cutting the hair short as a trope tells us that the character is in an extremely stressful or even traumatic situation and is trying to regain a sense of control. That's a complex situation but can be told in seconds by relating to actual reality.

It's not a trope in reality but it is one when used to convey a characters emotional state in a story.