I would never recommend a player start off or become an Oathbreaker. Also, you have to consider how the oath was broken. If a person made an oath and then (through no fault of their own or foreknowledge or inaction) couldn't keep it, I don't view that as a broken oath. Especially if someone got hurt while trying to meet their bargain. Magic (and therefore oaths on magic) are about intent, not just effect.
Also, practitioners don't **** around with oaths they swear on their power. They do their best to be very precise with them. Instead of "I swear on my power to protect you," they say "I swear on my power to be my best to keep you safe from X until Y."
But if someone wanted to be such a character, they can definitely start off with a filled consequence (there is no rule saying you can start with consequences, but it isn't like consequences automatically go away at the end of a particular story).
As an alternative (or addition) to effectively reducing skills is a straight compel - limitation. The only problem here is that it doesn't make more serious consequences have more impact (Oath Penalties seem to go away really fast once "forgiven"), but I guess higher consequences could just be compelled more often.
Maybe something like, Mild can be compelled once a session (but that seems weak), Moderate three times a session, Severe once a conflict, Extreme every time. Maybe Mild is once a scene, moderate twice a scene, severe three times a scene, and extreme is every time?
But there is still the issue of how important an oath is. Is the first broken oath a mild, then upgrade to moderate, then to severe, then extreme?