I notice that when germinating many larger seeds, once the spout
emerges from the soil, the seed case often sticks to the leaves that
are trying to open.

Spray the stuck seed case with water several times to soften it.
You will damage the cotyledons if you cut or pull.

That's a good idea. It certainly seems possible to damage the plant
pulling them off manually, as there often isn't much you can hold
onto.
Colin
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Replace the obvious with Bigfoot