Wow I am really happy to see that we have some conversation going here because I have been thinking about this a lot lately.
To clarify, I reviewed my ideas and I think that I can only go so far in explaining what I had in mind without possibly drifting into the territory of demonstrating how to manufacture machine guns, and I am not sure that's allowed here.
The basic idea would be to have a simple locked breach (either a rotating or tilting bolt, or a roller lock design) which is in a bolt carrier group that is also integral to an electromagnet assembly. The assembly would contract and pull the bolt out of battery against spring force, eject the Shell, then return under spring force while pulling a subsequent cartridge out of the magazine and clambering it like a standard firearm. The sequence would occur electronically, and would not be based on cartridge case head pressure or combustion gasses. When the trigger is pulled, and button is pressed and either a conventional firing pin assembly would be released or an electronic system like the one from Remington (RIP) would ignight the primer. After a pre-set amount of time which would depend on the specific cartridge the solenoid bolt assembly would retract and unlock the bolt repeating the cycle. This timing would be accomplished by an onboard microcontroller.
After reading your posts I think that really there is only one advantage here.
Cost and simplicity:
This design can be thought of as an improvised firearm like the ones found in many third world countries, there are fewer machining operations and less metal needed to make complex mechanisms. These countries often have excess electronics available and constructing a simple timer or circuit of the like is not hard. The cost of the electronics involved are much less than the machining time needed so for a home shop or a small operation the manufacturing costs and time can be reduced. You could even take it a step further and apply thus to 3d printed guns and make things even cheaper and quicker. I have no basis in fact for this but I think you could make everything except the bolt head, barrel, and magnet stuff out of plastic because the upper receiver does not have to support the stress of a blowback or other mechanism since the rechambering could be delayed long enough for the chamber pressure to get to zero at the expense of rate of fire.
To sum up I thing this idea really only works in the context of "I have limited tools and money but I want a select for gun that isn't an open-bolt-fixed-firing-pin grease gun type" then i think this is a viable solution.
Someone will have to help clarify what is okay for me to post drawing and math wise from my design process with this stuff. I don't want to get in trouble legally or on the forum.