you can't have it both ways; on the one hand there is a demand to have 'absolute numbers' so that they are relevant and on the other hand folk slag off the Chung method and similar, even though that (and similar) are amongst the few methods likely to give real world results. [BTW my understanding is that the Chung method produces results that are statistically significant after repeated runs, and then only if you can keep your errors under control.]
No one thinks that riding over rumble strips is representative of normal riding (and therefore why worry especially about absolute numbers?) but it does illustrate what is going on. All Heine has done is illustrate -for the benefit of those who have never noticed previously- what every thinking cyclist has known for years, i.e. that whenever you are being jiggled around on the bike it is probably costing you energy. Just holding the handlebars differently can change this, which rather underlines the futility of wanting 'absolute numbers' to play with....
My advice is that you carry out your own tests -on your bike, on your roads- to see what is going on and whether it might be significant or not. My take on it is that provided you are not demonstrably slower using the wider tyres (eg during coastdown and rollout tests), you are probably better off overall in any kind of distance event. This relies on another imponderable (which may vary greatly from one rider to another) which is that after a long day in the saddle "more comfort = more speed".
BTW there are further points which should be acknowledged and may be signficant for some riders/events; of these an important one is to acknowledge that you only get to go down the road at all because there is a torque transmitted through the rear wheel. Most Crr testing blithely ignores this altogether, in that the only torque transmitted though the wheel is enough to overcome rolling resistance, not propel the whole bike, i.e. the real force is probably about x10 or more higher. The real situation is much worse than that, because the effort is rather 'pulsey' in nature. If the tyre slips at the contact patch even slightly, or the transmission/tyre carcass deforms under torque loads in such a way as it doesn't conserve energy, every pedal stroke could be costing you.
In illustation of this, everyone knows that with suspension of any kind 'bobbing' is the enemy when climbing. IME you can 'bob' on fat tyres just as easily as on springs. If you do enough MTBing you also come to realise that a 'stabby' pedal stroke up a steep climb is usually a lot less efficient than a non-stabby one; with the former you can often see that the tyre is trying to break traction with every pedal stroke and this just costs you effort. [BTW in a comparable way, belt drives may measure low losses under constant torque but are pretty hopeless whenever the torque varies.] The other thing that becomes apparent when MTBing is that if you don't need super aggressive tread, the life of rear tyres will most often be limited by the carcass. When they will wear out in the carcass, it usually happens in such a way as they fail because of deformations induced by the torque loads passed through the tyre during climbing, i.e. the bias plies fail mostly in one direction only. The next time you ride an offroad climb, take a look at what is happening near the contact patch of another rider's rear tyre; it may surprise you. These things are also happening on-road too; although they are much less easy to see, they may be no less significant. For example I don't think it is a coincidence that, on the road, I've never climbed well on fat tyres, and likewise quickly sensed that riding with a belt drive is like pedalling in porridge; the two things can feel comparable to one another, which if it is borne out in reality means that there ought to be an easily measurable difference, if only the right tests are done...
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FWIW there is something to be said for training on bikes with suspension and fat tyres etc, even if you don't plan to use them during events; speed per se isn't really important during training and less fatigue may mean that you can train better for longer, and recovery is accelerated too. Educating your body so that you naturally pedal smoothly is certainly no bad thing if you are planning on riding distance events.
Anyway plaintive cries for 'relevant, absolute numbers' from a one-page article are IMHO just a waste of breath; reality is a lot more complicated than that and varies enormously from one rider/bike/road/riding position to another.
cheers