In popup I can't disable Text. I must delete it after inserted. Why?

I guess it was just created this way, assuming the text would always be included, with the other options as additional information only.

I may change it, although I'm not sure how this would affect selection when editing.

You can use css to hide the text, which is probably easier that deleting the text of each new link. Add the following to your template stylesheet:

.wf_file_text {

    display: none;

}