Based on the development tradeoffs, we've come to the following decision for the time being:
When 3D Preview is Off
We will continue to have the <#> identifiers, for now. We will at some point probably remove them, but not as part of this exercise, and in conjunction with making clearer ways to identify which geometry in the dialog corresponds with which geometry on the model.
When 3D Preview is On
We were going to show just "Edge" or "Face" for example. Our concern was that leaving off identifiers, by necessity, only when 3D previews are on would be confusing. Hence the discussion to rip them out everywhere. However, after investigation this is perhaps a change that has some unintended side effects and for this release cycle we will simply append a * to the input box geometry. So it would look like:
Edge*
Edge*
Face*
Edge*
The * indicates that the entity is no longer visible on the canvas, generally speaking, because it has been consumed. For example, if you select an edge to fillet and 3D preview it, that edge isn't there anymore. Turning off realtime previews returns the <#> text to the input dialog.
We will continue to evaluate ways to make it more consistent and take a more holistic approach at some point in the future. For now, the * should provide enough indication without cluttering the dialog.
Thanks for all your feedback here, we will incorporate it into future modifications to this UI. I will lock the topic now.