On the page of tasks itself, there is no button/link to display the logs from core_task_logs here.

This (to me at least) seems to be something to consider adding here; as if for example you view your moderators and/or administrators page, you will see a link to view those logs. Same if you go to  "Spam Prevention" one of the buttons will display the logs for that area. A lot of the suite quite rightly works like this.

I do realise the cron/task logs are not an interesting thing for most to view but it does seem quite logical to have it on this page, limiting it to only showing the last 30 or so entries seems quite sufficient as anymore and there's always other methods to view them. I'm well aware its not going to log anything for successful tasks, I did consider it possibly should but then if that happened the 'last x' entries would likely just be "task (name) ran without problems" so it would negate its own usefulness.

Quick crude pic:

 

As an alternative idea instead: How about having it on the support page instead (where it would be easily viewable for those who wanted it) under the existing two options. Another quick crude pic:

Thank you for considering this.

In your screenshot, you click the magnifying glass icon next to an individual task to view its logs (rather than view all logs for all tasks).

18 minutes ago, bfarber said:

In your screenshot, you click the magnifying glass icon next to an individual task to view its logs (rather than view all logs for all tasks).

I know I was after a some kind of listing similar to the other logs really.

Was just an idea. 🙂