Absolutely yes, self defense should be integral part of training for the security professionals, it is crucial skill set like first aid, firearms handling and many others. Every professional in the security industry must working on his CPD, including self defense skills and also keeping good physical fitness.
It would seem that many training providers are simply content to just train their candidates just enough to know physical intervention and conflict management to barely passable level.
Self protections skills should be the first part of training followed sharply by Third party protection skills all of which takes considerable training and continental improvement and refinement. That can't be taught on a CP course of minimal hours currently thought of adaquate.
In short YES! you should! This training cannot be a day added here and there, or a few hours introduction course it should become part of your life if you take your job seriously. I wrote a blog regarding this a while ago, you can read it here https://www.linkedin.com/pulse/whos-protecting-you-shaun-gowland?trk=mp-reader-card
I was talking to someone in the NHS who was doing their compulsory control and restraint training that all front-line staff had to do. Not security staff, medical staff. It was a 5 day course with a 2 day yearly refresher. If an NHS trust considers it essential that their staff are trained in control and restraint then it shows how remiss the security industry is in their attitude.
I have come across CP "experts" that say they don't need it because if it gets to the stage where you need to use force then you can't have done your job properly in the first place. I have to wonder about how they actually assess threats if they think you can't ever have situations where some random chance leads to someone having a pop at the principal.
Then there is the attitude that you can always talk someone down. I've even had this from DS trainers and people running security companies. When dealing with people on alcohol and drugs, talking often isn't going to work because they can't actually process speech. When someone is beating someone else up, you can't exactly say "Excuse me, could I just have a word."
Even if we assume that you can largely control your environment, every single workplace has to have a first aid kit and a first aider. Do we say that their health and safety procedures must be bad if they need first aid provision? Of course we don't! That is in situations where any accident is caused by some level of carelessness, however small. It is not looking at the situation you have in security where your job is to deal with people who are criminals and therefore have a fair chance of being violent to you or others. If there was any other industry with a safety hazard which did so little to train its staff to deal with that hazard, then they would be getting prosecuted.