Are there any characteristics that make it unsuitable for this kind of application?
As a minimum it looks like I need to put some diodes across the shunt to protect the op-amp inputs during short circuit events.
Depends on supply voltage you're measuring.
There can be 26volt between the two INA219 inputs (across the shunt),
but they can't be outside -0.3volt and +26volt.
See the 'absolute max ratings' table in the datasheet.
Leo..