Don’t the small wires have a big resistance?

Short answer(TL;DR): No, most loads are low Current and Current is affected by the wire resistance.

Longer answer: Cat5 wire is 24AWG with 40ohms resistance/1000ft. A 70ft run in a home loses 0.252 Watt for a 12W light, or about 2% of the efficiency loss for that fixture. AC LED bulbs have negligible wire loss at the expense of heavy copper wires and their drivers are 89% efficient on average with Power Factor of 0.7, so total efficiency of AC is 62.3% compared to 84% for LumenCache after the initial AC/DC conversion (95% with Power Factor Correction, 0.97).