I used to subscribe to the idea that open carry desensitized people to all kinds of carry. While I think the idea is valid in principle, I suspect the problem is not enough people carry at all, much less open. Unless there is sufficient stimulus, it won't have a desensitizing effect. Instead, it will just continue to appear as an obscure, unpopular, unreasonable practice unjustified by mob opinion.
Because open carry is often ill-advised even where it is socially accepted, few people will do it and there's a proportionally greater probability that people will do it for the wrong reasons. So I've changed my mind. Instead of hoping that open carry would normalize all carry, I now think that we should instead hope that concealed carry will continue to have some normalizing effect on all carry, including open carry. Certainly, both concealed and open carry should be protected.
In spite of the egregious infringment embodied in carry "permits," I believe they have done more than anything else to normalize concealed carry. To the majority of people that fail to see that carry is acceptable for all free people, permits give the perception that carry is "acceptable" provided the carrier has a permit. The warped thinking of many people is that a person needs permission for something unfamiliar to them to be acceptable. We see that with other things like service animals. Some people are really determined that a service animal must be "certified" and given permission by some authority to be legitimate, even though US law does not support this idea at all or recognize any certifying authority. We also saw it with "medical marijuana" cards for a while. Basically, the cards gave permission to the holders to do something that most people were conditioned to think of as illegal and illicit. If it was somehow justified by some (medical) authority, then it was acceptable. The remarkable thing is, as un-"certified" and un-"approved" service animals, especially those for invisible disabilities, are given public access, and more people are smoking dope without any kind of permission, the perception that these things are corrupt and illicit may be increasing.
For the record, I'm not a drinker or dope user, but it is a curious requirement for a CCW permit in my state that the permit holder not use dope even though the same state has a statute establishing the lawfulness of recreational use. Now the permit also forbids the use of alcohol, but only while carrying the gun, whereas dope use at any time precludes a person from obtaining or keeping a permit.
While "permission cards" have done a lot to normalize and increase the popularity of concealed carry, they have also reinforced the idea that permission and approval is necessary for legitimacy.
When I visited a Disney property, I realized that they had created a sort of utopia for their guests. More than anything, this utopia consisted of someone other than the guest being responsible for everything.. It's under those conditions that a lot of people feel secure and "happy." Unless this is changed, no amount of desensitization will content them in a world where they must be responsible for themselves. They will certainly want someone else, if not the government, then Google or Apple or Disney, etc. to take all the responsibility, and they will gladly hand over everything that's necessary for them to do so. They fully expect that they will need to be submissive and supplicant and are ready and willing.