You have to be assigned a free public defender by court, requiring a hearing, before you have one to call. That makes it impractical to use one when you are detained without being brought before a magistrate, even if you have the opportunity to make a phone call.
They don't just give them out when you get arrested. Often you have to file paperwork, prove you're indigent, and prove you made an effort to hire an attorney.
Moreover, most public defenders are overworked. They will do their job (hopefully), but they are not your secretary. (I'm sure most will make those phone calls, out of being a decent human being, not because it's their job)