Electronic – Why is the homemade pulse transformer so inefficient

For "concentric" wound transformers, I find both ways of them to be used, and the factors influencing it are most likely (may not all apply to your case):

• Cost of the material involved. Higher current needs thicker wires, but the same number of turns (and even thicker if its on the outside because it is longer there). Just calculate what is needed for the number of turns required in either inner or outer layer, and then do a comparison. It seems to me the higher the step down ratio, the more beneficial it is to keep the high current ones inside.
• Tapping. A lot of transformers have multiple tappings. Precise positioning and space for them is a lot easier on the outside than it is on the inside.
• Serviceability and failure modes. Bigger transformers are actually so expensive that it might be feasible to repair them. Depending on the expected failure modes putting one or the other winding on the outside is more useful.
• Rectangular cores might need different material strenghts and properties since internal forces are higher than in circular cores. Aluminum might be better suited here than the softer copper. This applies of course only at rather high currents (that are distributed unevenly in the conductor). Metal fatigue considerations however might drive you away from aluminum here.

Note that I don't call them secondary/primary but low/high voltage sides, I think those factors are more influential than the direction they are used in.

'Copper loss' is I²R power loss in the windings due to current flowing through them. As this current increases with higher loading, so copper loss also increases as loading increases.

Eddy current loss is power loss in the magnetic core due to current induced into it (each lamination in the core is effectively a shorted turn, but the silicon steel has relatively high resistance which keeps the current down). The induced voltage - and thus current and power loss - doesn't change with loading because the magnetic flux in the core doesn't change. This is also I²R loss, but it is not copper loss.

To summarize, there are two places in the transformer where I²R losses occur - in the magnetic core and in the windings. However, only the windings have a power loss proportional to load current. That loss can rightly be called 'copper loss' because only the windings are made of copper.