How commonly does a repeat instance need to be removed in your context? Can you please tell us about how the need to delete is discovered and what the user does next (e.g. do they add a repeat to replace what they had before)? There's the potential to lose a lot of data when deleting a repeat instance so there are tradeoffs in exposing it more.
Interesting! We must not have tested with a blank repeat label. Yes, we can make a better generic prompt in case of no repeat label. I'd also recommend specifying a label for the repeat so that it can be used in this context. We have this described in a note at https://docs.getodk.org/form-logic/#user-controlled-repeats and maybe we should make it more visible.