I believe that is all true, but I would caution people against treating "psychological reasons" as an afterthought (or worse, a point of scorn). I'll give you two reasons why:
1. The first is practical: Any one of us can fall victim to our emotions and end up making an error that hurts us more than holding a modest amount of bonds would have. I include myself in that, and I don't think a person is doing themselves any favors by thinking otherwise.
As an analogy, I'm currently dieting to take off a few pounds I gained over the winter. Now in theory, success in dieting is all psychological. I possess all the knowledge I need, it's just a matter of whether I can resist temptations and follow through. In reality, the psychological part is tough, so I employ all sorts of strategies to make it easier: I keep less food around the house, I restrict the hours when I eat, I switch things up occasionally to avoid boredom, and I stick to foods that make me feel full longer. If I were some perfect cogitator, I'd just calculate the minimum amount of calories and nutrients I need each day to function, and just eat that in the cheapest way. However, I have enough experience to recognize my own weaknesses in this regard. I try to design a strategy that is optimal based on my own characteristics, because trying to follow the strategy that is optimal for someone with perfect restraint would ultimately lead to failure.
Investing is not so much different, but due to the fact that we've been in a bull market for many years now, a lot of younger investors have not had a chance to gain experience from a bear market. Hence, it seems to all of us that resisting psychological impulses must be easy, so why not optimize as if such things don't matter. I'm sure there are some people who will find it easy to resist their impulses, but they are probably in the minority. If holding a few bonds helps a person avoid a bigger mistake later (like pulling out of the market following a crash), then it's probably a good thing.
Now, I'm playing devil's advocate here a bit, because I think there are other things people should focus on to mitigate behavioral error before going to bonds - for instance creating simple, hands-off portfolios and reducing consumption of market-related information.
2. The second point is philosophical, and I'll be less long-winded about it: Accumulating wealth through investing is a means to an end, not an end itself. A large part of that end is psychological - the comfort of feeling safe and secure in your ability to provide for yourself. It is logically consistent, then, for someone to adopt an investment strategy that is less volatile if it still keeps them on track to meet their goals while giving them less stress. Optimize for happiness, not account balance.