I know of a few who people travel with a personal smoke/CO detector, although I've never seen one on a Liveaboard. It seems to be more common when traveling to those remote backwaters of the world where safety can be an unregulated afterthought. People who use Airbnb frequently are also known to carry their own. I'm not sure how much value it would be on a Liveaboard, but one of the mariners here would have speak whether there would be any objection to this.
There has been a lot of discussion in this thread about what the boat operators can do, but was going to make much the same point that
@Ken Kurtis did above. There is a lot we can do as divers -- i.e., actually paying serious attention to the safety briefings, personally testing the escape hatches to ensure that we can work them, and making a note as to the location of exits, fire extinguishers, etc. We can avoid knock-off chargers and batteries, use fireproof storage and charging containers, and monitor the batteries we're charging and promptly unplug them when they're done. I'm sure if we think about it, there are many other simple ways we can help make these boats safer for ourselves and others.