It does seem more logical to be able to transplant the entire seed starter container, whether it's an eggshell seed starter or paper egg container seed starter because those can be set directly into the dirt. However I have tried the egg container method before and not been successful with it at all! The humidity levels here are too high and I tend to over-water, so for me the paper (or cardboard) of the egg containers tend to attract mildew.
I prefer the plastic seed starting containers that I find free from time to time. They look like this when I'm cleaning them & filling the cells with seed starter soil
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Yes the upside down containers are drying though not sure why I dry them before I fill them up with seed starting soil just to get them wet again. It's just become a little routine - out with the old, in with the new! Once the seeds are sown and sprouting they look promising:
Those are ice-cream sticks for seed labels, which work wonderfully! I do use Sharpie pens because even with weeks of watering over the sticks the plant names remain easy to read.