Signal processing can actually give you a truer representation of what an acoustic instrument sounds like. Unless you're in a studio, many times you're at the mercy of the room, other instruments and their amplification bleeding over into your mic, and what you record with as far as a mic, preamp, compression, noise gates, EQ, etc, is far superior to what you might have on the road. So taking a mic out of the equation, and instead involving a pickup which essentially is picking up the response of a metal string over a magnetic field removes the environmental variables much more effectively and make pickups a much more viable alternative for many, especially for musicians playing in a sonically vibrant atmosphere with a full drum kit, amplified guitars, keys, horns, etc.

In the end, it's really a decision one has to put a lot of thought into as far as exactl which path you go down, and even more so when you're on a budget.

Just my .02.