Thanks for the note. Yes, I agree with you based on flex, yet the downside is that, when skiing fast in cruddy conditions, I need the running length that a certain length ski gives me. I really liked that Mantra in 170cm (too much ski in 177cm) but 170cm can toss me around in cruddy snow, which is why I wouldn't buy a ski of that length. Likewise, the AC50 is great in 170cm, but that is more of a carver, and for frontside use, 170cm is plenty of ski. The real key to finding the "perfect" ski is getting the running length required for your conditions (shorter if you live somewhere that doesn't have new snow, has small hills, has tight spaces), or longer based on how fast one skis and how skilled they are (I skied a few runs last year with Eric Deslauries and he is a little shorter than me, weighs a bit more, and was on 191cm Sollie Shoguns for an all-around soft snow, crud, and bump day-being a world class skier has it's benefits). Once you have that dialed, the next step is getting a favorable flex for speed and skiing style, as well as height and weight. I don't think anyone can say exactly what that is for every ski they are interested in, without trying a bunch of skis.
With regards to overall length and flex: most skis don't change layup in different lengths, so their flex (deflection under force) won't change. What does change is that a ski with a really stiff tip still has that stiff tip, but it is closer to the skier, and easier to get to the front of the tip and pressure, as well as tip it. I would argue that I am not flexing a short ski any more than on a longer ski, but I am engaging the tip on a stiffer short ski in a different way than, say on a longer ski, with softer tip, where I can do that "pedal move" where I relax, pull back, pressure the tip, then push the feet forward to engage. On a really stiff ski, no matter the length, I have trouble doing that, and end up skiing more sidecut and less dynamically.
To answer your general question, I arrived on what is the "correct" length by trial and error. I found the skis that work well for me in a given length and those that don't, more or less. I wish I could come up with some magic formula, but am afraid I don't have one. With that said, there are skis that work in more than 1 length (such as the Blizzi 8.1 in 172cm (frontside carver) and 179cm (really stable all-mountain ski). I have typically found a running length (approximate, of course) that works well in softer snow to keep me up and keep from fighting tip dive.
OTOH, think we we define flex differently. OK, let's say construction won't change, although it seems a bit murky whether makers try to create the same handling for target skiers appropriate to each length by changing stiffness, sidecut, or whether they let length itself take care of that. Anyway, resistance to bending - called the second moment of inertia as I recall - will be determined purely by cross sectional area, shape (I-beams versus rectangular say). It has nothing to do with length, far as I can tell. So you're right. But the force that will overcome that resistance is partly determined by skier weight (M x a), yes? OK, hold that thought.
Second, polar moment of inertia, vaguely recall you have to tweak it to use for non-circular cross sections, will be resistance to torsion along long axis (think twisting a towel between two hands). So in theory length matters for torsion.
I'm also thinking that the actual force being applied against resistance is relative to sq cm of running surface, which will change as the ski gets longer or shorter, and that everyone in the known universe seems to think that heavier guys will flex a ski of given length more than lighter guys, especially the folks making the skis, but maybe they're calling something else flex. Not sure.
The real issue for me is about ski makers. I just don't get the disjunct between the examples you're giving and the lengths that ski companies offer. Let's take the Blizzard 8.1 in 179. You like it as an all-mountain, no issues with tip dive. The 172 is better for carving. Well, the longest length the 8.1 comes in is 179. And everyone in the known universe agrees that the 8.1 is a stiff ski. Forgiving in some ways,yes, but light and stiff. Now the (hopefully) bright engineers at Blizzard designed four lengths of 8.1, apparently to accommodate skiers of different sizes, or more accurately of different levels of force production (M x a above) that will deform the cross section of the mid ski.
So what you're saying, really, is that that the longest is appropriate for someone in the 25th percentile for weight who skis fast and doesn't want tip dive. OK, by extension, that means that the 158 is for children under 50 lbs, the 165 is for midgets and women with eating disorders, the 172 is for light males or normal sized females who stick to carving groomers more slowly, and the 179 is for light males who want an all mountain ski. Apparently the engineers at this point went home for dinner and forgot the next am to make lengths suitable for average sized skiers who ski moderate to fast speeds. Let alone heavy guys. Really dumb of them, huh?
Do you see my problem? (Well, this one out of many ) For all the discussion of tips and running length, the logical extrapolation of your argument is that almost no ski company makes skis suitable for normal sized males who want to ski denser snow. I just am having a hard time buying it... must be missing something obvious (as usual).