Not trying to knock anyone's personal preference, but I cannot understand what advantages are brought by the blacked out rear sights on Caniks. For me they just slow down sight picture acquisition, it's much harder to make sure the sights are aligned correctly with no dots on the rear, especially in low light. What am I missing? What makes these the new hotness?

I prefer a blacked out rear sight, u-notch. It's less busy for me and I can acquire the front sight faster instead of trying to align 3 dots. Personal preference.

Focus on front.  Helps with acquiring targets faster.

It's a competition shooting thing, a slim front blade with fiberoptic paired with blacked out rear allows fast follow-up shots once you're well practiced with it and focus on tracking the front sight.

So you don't get distract with the two rear dots.

It's easier for me to focus on front dot over target. Keep it simple. No rear dots.

Yes!  Much faster IMO.  Even before I started shooting competitively, target shooting never used anything but blacked front/rear.  When the 3-dot system came out, I tried but didn't care for the busy rear sight, so in a nutshell, it is a personal preference on which system.  The same goes for RDS on top of pistol, it is a personal preference IMO.

On my Canik, Warren Tactical sights set was included with fiber optic front sight and plain black rear sight as the TP9sfx is geared toward competition but I think all Caniks are equipped with plain back rear sight as standard.

I like it much better.  I really don't like 3 dot anymore.  4 of my handguns are now black rear sight. I feel its much faster.

As much as it annoys people who employ "shoot the dots" sight acquisition method for them not to be there, it works the other way for those of us who never used it.  If I am keeping a set of sights that has rear dots in place the first thing I do is paint them over and probably crack the tritium vials if present first so they never clutter my sight picture again.

I agree this is mostly born of the competition world where very few seem to use the shoot the dots method of sight alignment.  And probably worth noting that most competition is shot in broad daylight, not often in low light.

As for low light, I simply see a bright orange painted front with a tritium insert in a plain black U notch rear better and faster than I can ever align tritium dots, since align dots is a completely foreign sight alignment process to me at this point.

I actually agree with the OP.  I like my three dots on other guns.

This.
The various gun game disciplines have objectively demonstrated that the fastest daylight sight combination is a blacked out rear with fiber optic front. (Non optics obviously)
There is some room for debate on notch size, color and diameter of the rod, serrated vs flat, -which may be individually dependent on the shooters visual acuity and type, color or targets, etc.

Use whatever you shoot best with.  For me and my old eyes the fiber optic front sight and blacked out rear works best . However ,I have found that an RDS is even better for speed and accuracy now that I'm 70 years old and my eye sight has declined somewhat .