Traditionally, jiu-jitsu is performed right-handed: "there are no left-handed swordsmen in Japan". The jiu-jitsu syllabus is large enough that for self-defence purposes ambidextrosity is not required for many techniques: need the left-handed version of a technique? Use something else instead.
On the other hand(!) judo techniques are often practiced on the non-preferred side -- hidari in Japanese -- thereby developing the body evenly on both sides.
For me, one of the best reasons to practice left-handed is to increase one's focus on what you're doing. A reasonably well-grooved technique suddenly becomes challenging again. I find myself changing from side-to-side, engaging in self-observation and self-teaching as I work to transfer the technique to the other side. And the best thing ... the original migi side inevitably benefits too.
Other reasons to practice left-handed:
Injury: sometimes its unsafe to work on the regular side
Rehab: I have been working on one of my Chinese boxing weapon sets left-handed to try to stretch and strengthen a shoulder that appears to have sustained a (mild) injury
Teaching ploy: One of my students, who had previously been programmed to do a very different (Olympic judo) version of a throw, is learning our version in hidari first, as a stepping stone
In sum, I recommend occasionally training on the non-preferred side, as opposed to: never (traditional), 50-50, or mainly non-preferred (a competition-oriented strategy).