>  
> So, the coil losses decrease with it's L (assuming a given wire diameter, 
> coil diameter and spacing and so on) and thus it is good to decrease the
> needed L. 

You can decrease L only by condenser in parallel with a antenna.  But then
only part of coil current will flow thrue the ant (and ground stake also).
Let's describe some numerical example. Let antenna  capacity (denoted
as Ca) is 1 nF (large antenna!). Resistance of grounding we assume 1000
Ohm (huge resistance!). Parralel C (Cp) we assume to be 100 nF. Then L=3.2
mH. Let coil resistance is 1 Ohm (large coil!)  and coil current I is 1 A.
Then coil loss is 1 W. Antenna current for Ca<<Cp is (Ca/Cp)I = 0.01 A.
Grounding loss is (0.01)^2 * 1000 =0.1 W. With such a huge ground
resistance (unreally huge!) ground loss is only 10% of coil loss. 

Regards,
Alexander