Why brushless DC (BLDC) motors usually have low voltage and high currents? I am not an engineer, and neither familiar with motors, so bear with me. :) Thorough explanations needed. :)
The question is, why brushless DC motors intended for RC models and possibly paragliders rarely use high input voltage but rather high currents (and losing power to heat)? 
For instance, a motor consuming 144W would usually take 14,4V and 10A rather than 144V and 1A.
As I understand, raising voltage is more effective way to gain power for a motor than raising current (to a certain extent). I guess 300-400V is a more or less effective range. But there must be a caveat in this. Is it cost for battery/controller or something else?
If one is building a custom solution and not as limited in terms of costs, what would be the most effective way of transferring power from a battery to a shaft (with least losses) - raising current or raising voltage? Why?
 A: As long as you scale the wire size to always fill the available space for windings, the electrical inefficiencies in a motor stay remarkably constant as you rewind the motor for different voltages.
Take two identical motors.  Replace the windings in one motor with twice as many turns of wire that's half the area.  You'll fill the same space, but you'll need twice the voltage to drive half the current.  The resistance and inductance will scale up by a factor of four.  The $I^2R$ loss will be the same.  The ampere-turns will stay the same.  The back-EMF for a given motor speed will double.
What all this means is that the power generated will remain the same, and the power lost will remain the same.  You'll just be developing that power with twice the voltage and half the current.
The reason that the voltages are used in RC vehicles is one of convenience and, to some extent, safety.  As voltages go up, the transistor gates get ever harder to drive.  There's some steps in there -- 20V is one, and at least the last time I paid attention there was a cluster of ESCs and motors designed for four LiPo cells (17.8V at peak charge) while five cells (21V at peak charge) were a barrier.  There's a lesser one at 5V, which makes 1-cell ESCs simpler.
Basically, it's a tradeoff between ESC cost and complexity, wire size, total system weight, charger complexity (you can sorta-kinda get away without a balancing charger at 3 cells and below), etc., etc..
But it's not about voltage, per se., until you get down to so few turns that you can't pack the wire effectively into the space, or such fine wire that the area taken up by insulation starts to squeeze out the available area for copper.
A: A high-voltage wound motor draws less current for the same power output than a motor wound for a lower voltage. Lower current means less heat dissipation in the power wires leading to the motor, so thinner gauge (and therefore lighter) wiring can be used. In this way a high-voltage electrical system in an aircraft saves on weight. 
Since the control systems for small DC motors use transistors to switch and chop the power to the motor, and since power transistors for high voltage (>120V, say) are expensive, there is a practical limit to how much you can boost the system voltage in a variable-speed drive controller for a small DC motor; this usually works out to between 24 and 48 volts. Power transistors that chop 24 to 48 volts are extremely common and cheap. 
