
A quite secure (~80%?) position 1 center block blocking one side only takes a half second with a good split. A 100% secure one, both sides, still takes less than one. So as long as the enemy center and wings don't go super aggressive (in which case i usually do the short one and then try to center the enemy) it is possible to block it easily. I saw a picture somewhere showing it but can't remember where... maybe one of those fort blogs?
If the enemy centers nonetheless the sweepers can in most cases just block it (if no one died) or sometimes counterattack the center (if someone died) by digging that tail hard and turning towards him. If it's done on the correct side and the dig is enough (which is usually the case because sweepers should have more rubber available) then the enemy goes boom, fu, and everything is alright

And, finally, if those guys fail it, the defender can still get lucky and kill it

So yes, in my opinion it is the whole team's work. Wings split good, Center blocks. If he's going aggressive or when someone dies, the sweepers have to watch and act if they can. And the defense should watch if the sweepers are cleaning the situation, and, if not, react so the enemy doesn't get all of the zone.
Also, I don't see anything better the sweepers could do than netting a free kill and preventing a possible round loss unless there are enemies coming from other sides which is only the case when the wings fail.
The counterattack actually makes them join the midfield which does help in some situations.