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No, since the contact face has constant size which is mostly dependent on the air pressure in the tire, for fat tires, the contact face is 'shorter' but 'wider' compared to a slim tire. Thus, as less rubber needs to be deformed in rolling direction creating an angular momentum, they have lower rolling resistance. However, at elevated speeds of 20 km/h (~15 mph) and above, the air resistance, where slim tires perform better, becomes more important. Thus, racing bikes have very slim tires under very high pressures (also inertia plays an important role here).
Source: https://www.schwalbe.com/en/rollwiderstand , e.g.
I think there is an important factor you are missing here — although I fully acknowledge I may be missing something; I’m no tire expert.
Per your source, fat tires have lower roller resistance than narrow tires at the same pressure. A quick search shows that 700cc tires are usually run around 100psi. Fat tires appear to run at or below 30psi. Fat tires generally provide a cushier ride because they deform, but that deformation expands the contact patch and ups the rolling resistance. Are there super high pressure fat tires? I’m guessing no, but maybe that’s something I’m just not aware of.
I mean my mountain bikes run at a reccomended 50-80PSI, my road bike 60-120
I can also get up to about 40mph downhill on both (which should be a good indicator of rolling resistance/air resistance as it takes out the pedaling part), so that leads me to believe (given the rolling resistance info) that the actual biggest factor which makes the road bike so much easier to ride is weight (and gear ratios, but that's not relevant to e-bikes)
In this case presumably the MTB weighs more, which helps on downhills.
I think there's a whole literature out there on rolling resistance as it relates to tire size and pressure as a function of road quality
for really nice pavement/velodrome, skinny tires at high pressure win, but for rougher surfaces (e.g., chipseal or less than perfect pavement) lower pressures can be advantageous.
Thanks for that read