I imagine that someone, somewhere, is experimenting with this very idea. Recently I had read about research involving artificial wombs, something to replicate the natural environment of the womb, to help premature babies thrive.
An artificial egg shell would be useful for rare & valuable chick embryos whose shells suffer damage. Certainly those big commercial chicken ranches could find a use for them too.
There were some scientists that removed a piece of shell and replaced it with a piece of clear glass or plastic to watch the chicken grow. I believe they had a real fancy setup though to control the external conditions around the egg. When you do anything to the shell you can increase or decrease the moisture, air flow, etc... going through the shell and risk introducing bacteria. It's not something I'd suggest trying in a home incubator.
Once you break the sterile interior of the egg, the risk of infection is too high to make it reasonable. Recreating an egg shell also seems just not practical in industry because eggs are cheep, pennies cheap if that. As for rare birds, it would be more practical to reseal the cracked shell than to risk moving it intact in full to the "perfect" artifical one, since if the damage was so great to warrant egg transfer, the chick is probabably doomed anyways. A womb for human babies make sense to pour money into since research relating to humans directly is much easier to get funding for.
As for research, eggs are so cheap, I've gone though hundreds in just one week. Adding a window too an egg, ironically called "windowing" in technical terms, does work, but infection is high and hatch rate is dismal even done in sterile conditions. After windowing, you can't turn eggs well either, so that also makes it a bit tough.
I realize that there are definite problems with this idea, but I was just curious if the idea was probable. Im sure that someone has done this too. I like the idea and was intrested to see the embryo developing at a glance.
My thought was to use a clear plastic easter egg and then transfer the contents to the artifical egg shell. I dont think it would work but it intresting to think about!
You can transfer an egg into a stryofaom cup and cover with saran wrap to observe up to the first week of development. When ever observing development to study, you just incubate a flat (30) of eggs or two and crack them open when you want to see them. If you want, crack the egg into a dish at a certain date very carefully and you can pop them in the incubator and keep them alive for a day or so, more if you have a chick media.