It's a perennial question in the martial arts world and one that continues to ignite debate. In some places it also seems to have become an indicator of whether your art is effective or not, if it is "alive" - ie you work against a "resisting opponent"
First let me say that I'm not of the "too deadly to spar" school. This is often used as an excuse to never engage in any type of work outside of a fixed response pattern, which even at basic levels of training is of very limited value. On the other hand there are of course real safety factors to consider and no-one would suggest we regularly break each other in training in the name of "realism"
But if your goal is to study self-protection , sports-based sparring is of limited value. To begin with look at the range and set-up of sparring vs fight. Actual fight range is very close - I'm talking about a person intent on causing serious harm here rather than arguing or a pushing match. When a person is in the mindset of wanting to knock your block off they close in very quick. They want to punch, grab, bite, It's a very different experience from touching gloves then maintaining a safe distance while you feel each other out.
There is a psychological aspect to consider too. A highly agitated and aggressive person is acting off of primal instinct rather than a carefully though out strategy. That in itself can be overwhelming and needs to be prepared for.
In short there are countless variable factors to any situation, and we haven't even mentioned weapons or groups yet. None of these factors are replicated in the conventional "sparring" situation. One more thing to think about is that the sparring experience replicates only a very specific moment of any situation - the actual physical hitting/grappling part. If we are serious about self-protection we need a wide range of awareness and observation skills, how to read people, good communication skills not to mention a reasonable understanding of legal and associated issues.
This can develop into very sophisticated drills, such as the ones put together by Ed and Rory at this year's training camp, which put people through a range of physical and emotional challenges. As they ably demonstrated real self-protection work isn't all about being "tough" and charging through everything like a bear with a toothache, it is about having the skills to assess a situation and react accordingly. It's not often how self-defence is "sold" - people like an easy answer or a "no fail technique" that will get them out of trouble. The truth is unfortunately more involved than that, even the simple solution of giving someone a slap can have consequences way beyond the original situation.
So to spar? Yes - but with conditions. As with all training be aware of the strengths and weaknesses of the drill. Having a good ground grappling session helps develop skills and is a good workout (probably the most real you can get without injury). Gloving up and having a spar is good for hitting and getting hit, movement and developing tenacity. For instructors who run these drills - every now and then throw something different into the mix. Three people boxing instead of two. Chuck a knife to one of the grapplers. At least that will keep your people on their toes and stop them getting too "sparring" fixated. To take it beyond that start working the type of drill mentioned earlier, keep it safe, keep it challenging and keep it grounded in reality and personal experience - then sparring becomes a useful tool