Why do I feel like I'm talking to a wall? The point is not how much power the bike needs, but how much power the rider needs.

I don't deny that the power meter will quantify how much power the bike needs in order to increase speed. What I deny is the relevance of this quantity. Objectivity in itself does not mean anything. We could objectively measure the color of a bike with a spectrometer but that won't make it any more relevant. A bike without a rider that is both willing and able to produce the required power isn't going anywhere and unfortunately for us there is no simple and objective way to measure it because the will and ability of a rider to produce power is intimately mixed with many subjective factors in addition to the mechanical properties of the bike itself.

This just isn't true and it seems to be the main source of your confusion. As I already noted, it is simply an empirical fact that asking your muscles to produce a high amount of power for a brief moment (as when accelerating weights straight up in a gym) can quickly drive them from a highly efficient mode to 100% losses even if the average power is low. You can't argue with that.

They are not separate systems because forcing yourself to work harder to accelerate a heavier bike in the same amount of time will alter factors like muscle soreness, low blood glycogen levels, etc.

So it's not a question of if bike weight will increase the rider's mechanical inefficiencies, but how much it will increase them in typical riding. This is not a point of dispute, but a matter of fact.

And that's all it has to be. If an untrained cyclist is much less efficient then that difference in efficiency has to manifest itself somewhere. If manifest in the ability to cope with the increased demands of accelerating a heavier bike then we have an avenue for weight being massively important for all but elite racers.

You can say whatever you want, but the fact of the matter is that the biomechanical losses are not merely a fixed fraction of the power generated by your body.

As I've said many times, it only takes 0 watts to bench press 500 pounds "at the bar" which implies a 100% loss. Since biomechanical losses are not always 100% we know that assuming the power at the pedals is input power times some percentage is wrong.

The biomechanical losses obviously vary as a function of load. So if your body is losing 70% when generating 620 watts it may start losing 90% when generating 624 watts in which case you'd actually be getting fewer watts into the pedals. There's no guarantee that the power at the pedals is an increasing function of power exerted and we can actually observe this kind of phenomena when pushing yourself too hard actually reduces your capacity.

The biomechanical losses can also vary as a function of past inputs. So if your body is losing 70% when generating 620 watts right now, it may start losing 80% when generating 620 watts 10 minutes from now. So not only is there no gurantee that biomechanical losses are a fixed portion of the power being generated, but there's also no guarantee that the power at the pedals will even be the same when the same power is currently being generated and we can actually also observe this phenomenon as riders get tired over the course of a ride (or even tired from an initial acceleration overtaxed by extra bike weight).

Of course a trained athlete would be skilled enough to navigate around such dips in the function relating input power to power at the pedals, but that wouldn't be your typical rider.

And would it not bear to reason that untrained cyclists have a lower anaerobic threshold? I'd think that accelerating away 5 or 6 times over the course of a few miles could be enough to put most cyclists on the border right there. Not just club rides.

No, a typical rider is not riding for multiple hours at all. That's your problem, you think everyone is out there training themselves, riding around with few or no stops, and purposely putting themselves in only those scenarios where biomechanical losses due to bike weight and other factors can be minimized or eliminated so they can achieve their moment of glory for the weekend (for amateurs) or the day (for professionals). Not so.

I don't deny that Lance Armstrong's coach, Kreuzotter, or any of the other sources you cite are a good approximation for recreational riding with artificial rules and constraints, but I have no doubt that the artificial rules of racing, club riding, or any of the other pansy ass activities participated in by "cyclistes" have little to no bearing on vehicular riding in general.

But aerodynamic losses are more spread out compared to the effects of weight which hit you in spurts every time you accelerate. This makes all the difference. Everyone knows that interval training pushes your body harder (ie increases biomechanical losses).

You're comparing apples to oranges, but since you've weighed them both in grams you think they're the same. Your body cares just as much about when and how it needs to deliver power as how much power needs to be delivered.

You still don't get it. Viewing power at the pedals as the sole indicator of performance is an incomplete point of view. It's like saying $20 can buy you a soda at the soda machine. It misses the point because you can't use a $20 bill at the soda machine, but if you have quarters then you won't even need that much.

The fact that 1 watt at the pedals is the difference between you on tuesday and you on wednesday while 0 watts "at the bar" is the difference between the worlds greatest weightlifter and me means that the power at the human-machine interface is not what we should be looking at.

You're blinding yourself to the most relevant dimension of the problem. You think that since you have a $20 bill in your pocket you have enough for 10 sodas, but I'm telling you that since you don't have any quarters you don't even have enough for one soda. Needing to generate 200 watts is not the same as needing to generate 200 watts is not the same as needing to generate 200 watts.