Should I only post accessible apps to the AppleVis App Directory?

No. If you have found an app to be inaccessible, please do post details to the App Directory.

Knowing about inaccessible apps is regarded by many users of this site as useful and valuable.

Other users might be willing to tolerate issues with an app that you consider make it inaccessible. This is particularly likely with apps that have desirable features not found in other apps or where there simply isn't a more accessible alternative.

Alerting people to inaccessible apps can save them time and money. It can also improve the likelihood that the developer will do something to improve accessibility. Many developers have done just this after seeing problems mentioned on the AppleVis website.