Why are EI-cores (shell-type) most common for power transformers?
Two reasons. The EI core needs only one bobbin, and it needs less iron. See the attached pic of an EI core and an U core made of its parts.



See how the EI core only needs 28 iron units while the U core needs 36? (Of course this is a simplification but even when you round the edges of the U core you are still missing 4 units.)