I haven't used Unity's IK, but if this is the case, you can always write your own solution. To get AAA style sports-game animation, you'll probably have to write a hell of a lot of custom animation code rather than using an off-the-shelf solution
In my experience, sports games do a lot of intensive animation blending and state transition stuff that isn't required by most games / won't be supported by general solutions. Things like keeping track of which foot was the last on the ground and doing different blends based on that (which requires tagging the foot-fall animation frames and then all other frames with left-phase or right-phase), tagging frames for when the ball and a hand/foot should collide or lose contact, having a massive database of similar animations on hand and being able to quickly query which ones are the best to blend for different target poses, etc...
Ignoring IK for a moment, you can get a long way with simple animation blending. Say you want to write a solution for when the ball is going to pass through a 1m x 1m square to the right of the character. You could make four swinging animations -- one for hitting a ball at each corner of that square -- and then by blending those four animations with varying weights, you can generate a new swing animation for any other point within that square too! To get better quality, you can add a fifth animation for the center of the square, too (which breaks it into 4 triangles, so can also make it cheaper as now you only need to blend three animations).
You can also make single-frame animations which are basically just poses, or different ways of holding the racquet. By blending those in, you can change the angle at which the racquet hits. Also, blending doesn't have to occur globally across the entire skeleton. When blending animations you can restrict it to just an arm and fade out at the shoulder, or just the spine, or just the legs, etc... Again, you can either use unity's existing tools for this, or take full control and implement all of this animation/pose logic yourself.
I would try to do most of the work by having a catalog of every different kind of swing that you want your characters to be able to make -- enough of them so that by blending them together you can pretty much place the racquet anywhere. Then I'd add IK on top of that just to do any final tweaking that's required, NOT as the main technique for getting the racquet to the right spot.
Also, if you want to completely avoid the fake hit situation from the video you posted, you can detect when your animation system has failed pretty easy by putting a sphere collider on the racquet and checking if the ball actually hits/misses it. If the ball misses the racquet (because your animation code has failed to move it to the right place), you can choose to not apply your fake physics