When hovering over an Issue Link, rather than seeing just:

View this issue in Jira: XX-NNNN

You should see

Jira: XX-NNNN 'Summary text'

IF this was implemented across the board then many of the reports will be instantly more useful as you then don't have to navigate to different pages to see what ID XX-NNNN refers to.

A task ID on its own is much less useful in Agile development than it is in the Support environment. In Support the ID is often used as the basis for referring to a customer problem or ticket.

However, in Agile, the story summary is the main thing and IDs are more incidental.