I & every other repairer fit dozens of tyres every year.
Never had a egg shaped tyre from cheap 2 plys to expensive 4 ply.
And yes they arrive a funny shape & often I have to put a tube into the tyre , blow it up & leave it in the sun for a day or so for the tyre to go back into shape.
But never had one that felt like riding on eggs.
A rough guess would be the hub bolt holes not being concentric with the axels or the rims not being square to the hub.