We have done regular live recordings of band performances over the years. Recording on location and later the final mix done from our studio. We had invested in a double Alesis HD24 hard-disk recording set up especially for this branch of sport.
The 2 coupled machines were neatly in a flight case, along with the right number of pre-amps. This set up went to the place of the concert and was linked to the stage set up on stage by means of a splitter. Microphones and DI boxes intended for the PA were given a double function in this way. It was a lot of work, but the result was good. The registration of the direct microphone signals was later unloaded in our studio in Protools for the final mix. Nowadays this is much easier. Most venues work FOH with digital tables, where you directly attach a laptop. Signals are leveled through the table's pre-amps and passed dry for recording. You only need to bring a hard drive to take the recordings to the studio for the mix.
Actually, this is a very effective and relatively cheap way to capture the magic of a band. We were one of the founders of the rock band Voltage. We made live recordings at Muziekcentrum De Bosuil, which later became part of Rock Inc. Recordings are mixed.
Because the band had their sound well organized and played very tight, mixing was a joy and a representative, honest and atmospheric live demo was created. If you choose this way of recording, it is a must for the band to take the stage well prepared.