How recent is your experience with "traditional" phase detect/contrast AF? There's been some ridiculously good improvements even in the past 12 months in cameras like the Nikon D850/Sony A7 XXX, to the point where fancy "lightfield" style setting focus in post like the Lytro is way lower on my personal wishlist than it once was. The eye detect AF in the Sonys is frankly superb when working with extremely shallow DoF. This stuff typically filters down range to cheaper models really quickly as well.

It's a recent camera but not top of the line (Fuji X-T2).

My problem is more that with animals, it's hard to make sure it's picked up the head vs the shoulders, say, and with shallow DOF that can ruin the shot. But then, I don't have eye detection, so maybe that would do the trick. :)

The v1, at least, wasn't great for action. It has 10 focal planes, but they cover a fairly small range of distances, so it still needed an autofocus to get the range of focal lengths to be centered on the subject. And that autofocus was pretty slow, even slower than what I'm used to on an SLR.

I'd assume the Illum (which I've never had a chance to play with) would be way better on that front.