Any discussion of the competitive cyclist fit seems to have most people saying it's pretty ok and a few folks reasonably pointing out that tube lengths are meaningless without seat tube angle (STA). Normally you would need both to calculate stack and reach.

However, what these criticisms apparently failed to account for is that CC also provides nose to handle bar (rear edge of bar), stem length, and saddle setback.

Reach=nose_to_bar +1/2 bar diameter - stem_length - setback

and maybe plus a couple more mm for the tilt back of the steerer as it rises from the headset bearing to the center of the stem.

Once you have reach you can work out the STA by working back to the x position of the top of the seat tube using the TT length, then combined with C-T ST length you get the angle. The vertical of that triangle then gives you stack.

From there you can also get the seat to bar drop although their seat height recommendations seem a couple of cm too long, so might need modifying. And then you can get the true nose to handlebar distance in 2d (not just the horizontal distance), which in principle could be the most useful bit of information it provides. Basically how far between you rear and your hands, to make sure your shoulders are at a good angle, something that probably can actually be calculated reasonably well. In my case it did seem to do pretty well at that, which gives me some reassurance on that aspect of my fit.

The question is does CC really use, under the hood, a detailed self-consistent geometrical model so that it even makes sense to read this much into it mathematically? Or do they just have some simple rules they've found that tend to guess each of the stated tube lengths about right on average for some common bike geometries?

Now, and this is my opinion (I think not too controversial), I don't see how a calculator can possibly know what setback or seat to bar drop you need, and thus how it could know even approximately what stack and reach you need anyway.

Does it know your weight distribution? Does it know how much you're willing to compromise aero for comfort with a forward position? Does it know how much you favor your quads vs glutes or how much stress you like to put on your forward saddle bits?

It's telling me I need 5cm of setback and to me I feel like I'm falling forward off my seat at 5cm. It's not a very generic all-around number either, although it might be close to KOPS for me. I can hold that position even without touching the bars because I have enough core strength, but it certainly takes more effort/energy and I'm not a competitive racer.

If you need more setback you're surely going to need a relatively shorter reach to compensate, or a shorter stem at least. I don't see how you can even ballpark this. I guess if you put everyone 2.5cm behind KOPS you'd get within 2.5 cm plus or minus for most people, and if you calculate for a 110 or 120 stem they'll have 2cm of reach adjustment either way left up front, barely, or compromise a little on both setback and reach, but almost anyone can probably guess a bike size by eye if that's good enough.

And clearly a calculator can't tell anyone what stack they need.

Still, Competitive Cyclist technically does determine more than it's usually given credit for, if you consider it as a calculator that leaves much of the calculating left for you.