In a nutshell, we can stay silent so who cares?
The problem with that is that everyone should care. By the nature of their jobs, police deal with people with a variety of disabilities, levels of education and language comprehension. I don’t know that it’s reasonable to expect people to have the presence to remain silent. Yet if they don’t, we’ll happily incarcerate them. I don’t like crime but I hate innocent people being punished for crimes they didn’t commit.
Likewise, say it happens on a Monday. Your work is gonna wanna know where you are. They can definitely get away with firing you simply for getting arrested due to "At Will Employment" since you can't really go to work while in a jail cell.
While pleading the 5th protects you from the government forcing confessions or something similar, it doesn't save your job.