Published properties in OI are shown because they are part of RTTI.
If you need to know methods of some object, write NameOfObject.<press Ctrl+Space> and Lazarus will show them all.
Or simply hit F1 and - if everything is configured well - Laz. will open browser with documentation.
That's very true, and I use it to find public methods. But...
The completion list has ALL the methods and properties of the family tree right back to TObject. That is useful in many contexts, but downright frustrating in others.
My suggestion is more subtle, and would only apply to components in the IDE palette. The Object Inspector/'publish' directive would act in concert to display only the public methods the component writer tagged. (and ancestor tagged methods of course)
I think it would be genuinely useful when a developer first uses an unfamiliar component; kind-of in the spirit of RAD, and it involves very little extra effort for the component writer (just add the 'publish' directive to selected public methods)
I agree it's not a need, but a wish. (and would be another enhancement of Lazarus over Delphi)