If you feel like crying, but hold back, does that feeling just immediately disappear and you get on with your day? Of course not. You just bury the stress, and sooner or later it bubbles back up again in weird and unpredictable ways. Is crying at work more or less professional than having a panic attack at work and ending up hospitalised?
Crying is just an expression of stress. If your actual statement is that people shouldn't be stressed about non-work issues at work, then good luck, that's not how human beings are engineered.