It sounds in theory like a good idea, yeas. But then, there are the people who are actively involved in the clan side of things who would likely be annoyed if it were removed, same with the forum game threads. Just because some people are annoyed by it does not necessarily mean it should be nuked, potentially annoying other people.
As well as this, as has been touched upon above, XenForo does not really offer an option to exclude certain things from the Recent Activity and the What's New feeds. It probably could be done, but it would have to be done by manually changing the settings and code by one of the devs. which is really not worth it IMO - that's when things can become mucked up.
Another point to add - if you don't want to see the clan threads, simply browse by forum section.. sure, it may not be as convenient as clicking What's New and seeing every piece of new content, but if you click on a section if lists all the threads in order of last edit time, which is essentially the exact same thing.
TL;DR: Yes, it might make active forumers and people such as myself happy, but it would likely annoy others. And the devs time etc having to change XenForo = not really worth it.