The debate over the ideal martial arts philosophy for self-defense rages on, but Stephan Kesting describes mine more precisely and eloquently than I could: devote almost all your training time to training "safe" techniques with high levels of resistance and very little to "deadly" techniques with low levels of resistance.
Both philosophical and technological innovation have driven the ability to train "safe" techniques. Additionally, both have increased the scope of techniques that can be trained in relative safety.
Although it's not precisely clear who or when the first mouth guards were first used, the use of acrylic material in smaller, thinner mouth guards in 1947 propelled them from more limited usage to ubiquity among high school and college football players by the early 1970s.
Chris Haueter mentions that the invention of the closed-cell foam mat after World War II meant less injury and less discomfort for those training grappling on the ground. I can honestly say I'd be much less excited about BJJ training on tatami mats, canvas-covered sawdust, horsehair mats.
From an economic perspective, this has more of an effect on training accessibility than, for example, knee or elbow pads. The reason for this amplified effect is that it concentrates the cost in the facility and decreases the effort necessary to begin every training session. Both effects reduce the friction on the practitioner, and marginally increase the number of practitioners.
Although originally intended primarily to protect the striker's hands, heavily weighted gloves that diffuse the impact pressure over a wide area make bruising and cuts less likely in training. This widens the appeal of striking arts significantly, as many of us have to face customers and co-workers every day, and a beat up face is (for most people) cause for embarrassment, not a badge of honor.
Like amply-padded gloves, boxing headgear protects against cuts, scrapes, and swelling, although it does not protect against the direct or indirect effects of concussion.
Among grapplers, wrestling headgear is used to avoid the onset or reduce the severity of cauliflower ear. Again, while cauliflower ear has some appeal among a small subset of the population, the rest of us don't need any (more) points against us on aesthetic criteria.
Limit Dynamic Movement
As John Danaher explains, the first "step" in the BJJ formula is to take the opponent to the ground (about 3 minutes). (Note that this isn't always desirable for fully generalized self-defense training.) In short, the in-fight intent is to attenuate your opponents ability to generate dynamic, explosive force. Happily, this muting of dynamic force spills over into training, too. It's pretty obvious that limiting dynamic movement reduces risk in training.
Position over Submission
From a training perspective, the advantage of this philosophy is strongly related to limiting dynamic movement. An alternative, but much less catchy rephrasing, is "prioritize control over submission". This principle, whether intentionally or not, slows the pace. Consider, as an example, the likelihood of injury using the same submission technique, the triangle choke, but with two different preludes: