
In spite of the variety of electric guitars, violins and basses, acoustic instruments remain quite a popular choice for musicians. Their efectiveness in learning process (they uncover mistakes more accurately than electric gear), their reliability and the unique sound they produce are the main features that make thousands of them still being manufactured each year.
Queen used them quite often on early albums, but not live initially since they were harder to amplify: miking them causes loads of feedback, unless they very carefully set them up. In the studio it's not a problem since they could take some time to install everything around the acoustic guitar while Brian or John recorded it but live they didn't have got enough time or resources, especially considering that most of their setlist was still electric. The only acoustic stringed instrument they amplified that way was Brian's ukelele-banjo, since he only played it for some few seconds in Bring Back That Leroy Brown.

A good example is Crazy Little Thing Called Love: when recording it, Freddie placed external mics that sent the signals to the multi-track (allowing the guitar to be mixed stereo), so he had to sit and move as less as possible. That wasn't a problem for a half-hour recording session but to do the same on stage, would be rather risky and uncomfortable: he could accidentally hit the mic, he would have to be almost motionless, and there could be many noise problems because of feedback.
So the way to sort it out was obviously giving Freddie an electrified acoustic guitar (one with piezoelectric pick-up) which let him move around the stage, allowed better control for sound mixers and cancelled most of unwanted noises. Ovation guitars produce some very famous round-back electric/acoustic guitars which the band always endorsed: Brian and Freddie used them many times on stage and so did Roger during Happiness tour.

Obviously, acoustic guitars require different kinds of amplifiers: the ones made for only-electric guitars modify the sound to make it heavier and fuzzier; acoustic guitar amps have (usually) the only function of reinforcing the sound, as clean as possible.