Update: Since there was no objection to the creation of the tag and I can't think of a single reason not to have it, I now took the initiative and created banach-algebras and I will slowly start adding it to questions that should have it. If anyone else sees a question that should have the tag please add it but try to avoid flooding the main page by bumping too many questions on the topic.
I will soon create a new thread in order to discuss the ambiguities of some related tags I mentioned below.
This is not really an answer but far too long for a comment:
I don't think there's any other reason for the absence of banach-algebras than the evolution of the tags themselves.
Yes, having a banach-algebras looks like a good suggestion to me and its absence bothered me for quite some time already. I agree that all those questions you list (and many more) would benefit from the presence of such a tag.
At the moment I can think of the following tags with non-empty intersection with banach-algebras:
A while ago I or someone else eliminated the rarely used normed-algebras tag (one or two questions) because there seemed no need for that one.
I don't have a solution ready but I think the following should be discussed before action is taken:
I'm posting this answer as community-wiki so that others can add tags that should be discussed in this thread. Please do so.