Briggs & Stratton will not fire unless I do This....

Shouldn't there be infinite resistance between the one plug post on coil and the body of the coil?

Three parts to a modern coil.
All 3 of them ground out to the laminations
Primary
Secondary
Trigger

You can check the secondary plug wire to laminations with an Ohmeter.
You can not check the other two because the trigger module controls the grounding of the primary with an ohmeter.
You need to send a signal down both of them with some very expensive equipment.

AS all 3 parts are interconnected and none can be replaced as an individual part it becomes a moot point.
If it won't fire without the kill wire attached then it is replacement time.