I’m sure there’d be obstacles to overcome but in theory couldn’t couldn’t a piezo igniter replace a primer?
Machine a primer shaped stud centered on the firing pin hole of the bolt face
Put a powerful Piezo igniter inside the bolt so the igniter element will:
First move forward into the flash hole and then spark when you pull the trigger.
The primer shaped stud could be tapered slightly and forced / held tight in the primer pocket to seal escaping gas.
Rimmed cartridges would make getting a tight seal simpler.
Flash hole has to be centered exactly.
A foil seal in the primer pocket covering the flash hole to contain the powder charge in the cartridge case could be easily penetrated by the igniter element.
Bolt face, primer pocket and flash hole tolerances would be critical. A strong spark and durable igniter element and easily ignited powder are needed too.
If spark from piezo isn’t hot enough an old automotive condenser or small capacitor would throw a hot spark.
I have a can of FFF somewhere. Have to see if a piezo igniter spark will work on it or a fast powder like Titegroup.