E-I cores are flat stampings with no bending or forming needed, so cheap to manufacture.
They interleave in a way that allows simple corner fixings hold the whole thing together - or just vacuum impregnation with lacquer is sufficient.
The usual "E" interleave also means they have very good magnetic coupling between the two ends of the core, as the E legs overlap layer to layer.
Symmetrical C or U Cores need additional clamping as there is no interleave to give a mechanical joint, as with flat laminations.
Plus, the core-to-core joint is a flat surface, which must be very precise to get good magnetic coupling - the cores have to be ground or or finished in some way after forming to get a good joint, which makes them a lot more expensive than simple stampings.
I believe L cores are quite often used, but I think they are generally in welded core type transformers, where the core can be clamped for welding after assembly into the coils.
eg. - A C core type, with metal strapping to keep the cores in place: