Cruising is an extremely safe and relaxing way to travel. As PP said, people falling over is extremely rare - around 40 over the last 10 years, while there are tens of thousands guests sailing at all times - and they usually do so by choice, by doing something stupid (blame Instagram !) or in a domestic violence situation.
DCL has one of the best, if not the best, record concerning cleanliness of their ships and the respect of disease prevention rules. Their ships are also right in the middle of the passengers to size ratio standard for the cruise industry. The ships have limited passenger capacity and crowding occurs only at specific events that can easily be avoided.
However, as the local cruise expert at work, when I talk about my trips, I notice that some colleagues have an inherent fear of being on the open seas, somewhat similar to a fear of flying. Whether it’s the fear of getting sick, the idea of not being close to land, the realization that there will be miles of water under the ship, the impossibility of leaving the ship at all times or the fear of being in an enclosed and cramped space, no amount of reassurance or stories of wonderful service, great food, actual size of the ship or interesting port visits scratches the surface of that fear, and that’s ok.
They usually find something mentioned by OP - rampant stomach bugs, drunken passengers everywhere, exploitation of employees - to mask the real reasons behind their reluctance to sail. They know full well that those fears are irrational - there wouldn’t be a cruise industry if those things were real - much like fear of flying is irrational when you know how much statistically safer it is to fly on a plane than to do anything else in your life.
Unless a close friend or family member is getting married on a cruise, I don’t see how going on one could be mandatory. It is a vacation an no one should be forced to go on a vacation that involves facing their fears. If the real reasons behind her refusal are the things mentioned in your post, you can show her vlogs on YouTube and posts here and she should easily drop her misconceptions. If there’s something else, you should not try to guilt her into going and put her in a miserable situation.