What is the advantage of using self-resonant coils with distributed param over ......

I'm having a bit trouble understanding why the MIT team used self-resonant coils (essentially antennas cause they weren't connected to anything) over a conventional LC circuit?

In other words, an antenna radiates, and it radiates both E and H, where E is unwanted cause its harmful. But they chose to go with an antenna anyway, despite the fact that you could easily use an LC circuit where your L would be a big circular loop coil and a regular high power capacitor. Your E would just be confined to within the plates of the capacitor and would only get H field from the coil, which is desired for magnetic coupling.

But they used a self resonant coil with distributed inductance/capacitance and I'm not sure why they chose this. Is there any advantage of using this for longer range or efficiency or something? It seems to me like it would be a harder thing to design a coil with self-capacitance rather than just use the same coil with a real capacitor. I'm sure there's some reasoning for this but I have no clue :(