Once upon a time, our friends at the RIAA threatened to sue anyone who introduced a medium which could faithfully copy a CD... so, when DAT was being introduced it was greatly delayed because of fear of retaliation from the music industry. It was introduced with what is known as SCMS (Serial Copy Management System) as a compromise with the RIAA where only a single digital copy would be allowed on a consumer DAT. Professional machines were not restricted by the agreement with the RIAA. The first company to introduce a consumer DAT was Nakamichi with the 1000 but its cost was sky high (around $10K) and avoided problems with the RIAA. Eventually, the delay of DAT had killed its application as a consumer medium and became supported only in recording studios. CD-R followed close enough that it became the digital medium of choice for copying and we all know what has happened to the RIAA fears of piracy in the meantime.
For recording sessions, when doing a live 2 channel recording the CD-R is a very poor medium to use (dropouts, errors writing the CD-R, etc...). Therefore, DAT is very popular for this and has kept its foothold in studios and location recording. It is much cheaper to use than analog, much more robust than CD-R, and very convenient.