Yes. As you need separate set of permissions to replicate assets and tags. In your case you have permission to replicate both assets and tags. But that is always not the case.

I see same issue with Text Component across We.Retail, Core Components and also Text component under General Group

Yes. Same issue.

I see the same behavior on 6.4 OOTB. If I style multiple lines at the same time Lists icon is disabled on the first line. If I style each line one after another List icon is disabled on all lines.Also I see same behavior with Text Component under General Component Group (not just We.Retail component group). May be a bug.