Amplifying instruments by measuring current in conductive strings
Does anyone actually use this method? 


For stringed instruments, no, but the principle is used in many, many places.


  is it useless, so no one talks about it? 


It's not useless, but it has some significant disadvantages, and other methods are simply far superior.


  I tried it last night, and it works, but the signal is very low.


That is the main disadvantage.  Others are:


You are measuring low induced voltages in the string that is in contact with a conductor (human) which messes up the measurement
More advanced measuring techniques induce a voltage in the string, but again the human conductor is in the way
The strings are more variable in terms of electrical properties (resistance, capacitance, inductance) all of which affect the sound, and mean that two instruments might sound very different
The strings, being long, are not unlike antennas and inductors and are very good at picking up stray noise in electrical and magnetic fields.  You can be much closer to a lamp ballast with a coil pickup before picking up the AC hum than you can with a string pickup.
There's no galvanic isolation, so the amp has to be isolated from the AC line and high voltage sources, which pretty much rules out tube based amps.
Electrostatic discharge from the user into the string and conducted into the equipment is damaging, but even if it's suppressed you can't easily filter out the additional noise it causes.
Getting a good electrical connection to the string in a performance environment is difficult since it's hard to tin the metals used in many strings, and vibration, corrosion, and other environmental factors complicate it.


That's just the start.  Don't misunderstand, coil pickups have disadvantages too, but they are superior in many areas.