Am reminded of Dirty Harry asking
are you feeling lucky?
Lucky enough for the limb to not fall on a car or person in a storm, by some horrible twist of fate, like someone driving in the lane
in a storm? Within the last year this has happened multiple times in New England. Two people died in one car crushed by a tree.
If this broken limb is over your driveway, you have a dangerous situation in any upcoming wind event.
Rain will get in that big opening and rot the wood after awhile but I'm thinking
wind will solve the problem long before that.
I would not ignore it. It is a known dangerous situation and if you knowingly ignore it, your homeowners policy may give you grief if you have a liability claim. (many years as Travelers underwriter)
Front end loader and my man cage would make quick work of this. Mimic the pros like everyone has said, start at the end and work your way in.
Plan for the worst and hope for the best.
I take down stuff like this all the time here, with a big strong fireman in the bucket and me driving the tractor. Plus an Echo pole saw with a very sharp chain.
Undercut always, don't want the bark to rip.
I look at that tree and all I think is firewood. I might pay to have someone drop it, then I'd chop it up from there on. Once things are on the ground,
so much safer to work on.
This kind of work takes very strong arms and physical condition, I can't do it any more in the air.
so my advice to OP is if you need firewood, I'd pay someone to drop the whole tree, since it has disease issues already (?) ,
get it off the road, and then you work on it at your leisure.
be safe.