IMO, your best bet is to find a way to pull out the post with the concrete intact. Then replace the post in the hole and either refill with new concrete or to pack in some fill dirt.
There are various ways to pull out the post. One way is by using a front loader, a backhoe, a forklift, or something else to pull it straight up. I've seen some videos online about using a car tire/rim and a log chain/tow cable attached to a vehicle in order to pull a tree stump. The idea with the tire is that you put the chain as close to the ground as possible and the tire redirects the horizontal pull into a vertical pull.
Once you get the post and concrete out of the ground, you can dispose of it, without having to break up the concrete, in a dumpster or by taking it to the local landfill yourself. And if you need to make it smaller, you can cut the post easily enough, or if you do need to still break up the concrete, it's much easier to deal with. You can even use a tile or concrete saw at this point, even if it's just to make stress points, like other people were suggesting to use the drill holes, which could still be done.
I would recommend against using a log splitter wedge. They are sharp because they are designed to get in between fibers or to cut across wood fibers. Rock and concrete, not so much. If you look at a new masonry bit, you'll see that it's not sharp at all. It's not cutting, but rather chipping away the material, which is why electric drills for masonry and concrete have a hammer action. You can drill through masonry and concrete without the hammering, but it'll burn up bits really quickly. Been there, done that.
Most likely, you'll dull the wood wedge in the first few blows and end up breaking off chips, so it won't even be good for wood cutting anymore (at least not without significant grinding it back to shape). If you keep using it, those chips will lead to stress cracks which could lead to large pieces breaking off at high speed, or simply just crack the wedge in half.
You can even get wedge or spade bits (also not sharp) for hammer drills/rotary hammers that are designed to use only the hammer action, not the rotary action, so it's more of a small version of a jack hammer used in road construction.
What you need to break up the concrete is shear stress, where one part of it is stable and doesn't move while another part isn't supported. Often times, this is done by the large size of the slab of concrete it's poured as, but you don't have a slab, but a column, so that's more difficult, and it has a soft core of wood to help absorb vibrations. About the only way this is going to break up is of you have a slab of concrete that you don't really care too much about or is really thick, lay the post on the slab, then support only one side, then whack at it with the sledge hammer until either you or it gives up.
