Many of the Discussions are several years old and don't even pertain to the record they are currently attached to. We are allowed to change and update pretty much everything else in Family Tree. Why not Discussions?
You can contribute to discussions - you just cannot delete other's contributions to them. If they do not apply to the profile you can contribute a request to remove them - directly to the original contributor. If that contributor does not respond or is no longer living I don't know how you could get those changed - I guess contact FamilySearch to make such a request.
I'm sure there are many users who put their comments in Discussions precisely because they know they can't be deleted by others! There is an "Add Comment" box directly below, to which you can note whether the remarks are no longer pertinent, or if you believe the content is inaccurate. But, please, no - don't encourage the ability to delete Discussion items, many of which I have recorded to highlight important facts that really should remain to be seen.