Something not clearly stated is that 'rolling resistance' (energy lost to the flex of the tire casing as it rotates) is only a small fraction of the total drag on a bike. At normal riding speeds (above ~20km/h) your total aerodynamic drag is vastly greater than drag from rolling resistance. As speed goes up, aero drag increases exponentially and rolling resistance only increases roughly linearly. Wider tires can have less rolling resistance, but wider tires can also cause greater aero drag, esp. if the tire and rim widths are not a good match. And same as total aero drag, aero drag from tires also goes up exponentially with speed.

Also, all other things being equal, wider tires are heavier and will slow you down when climbing.

'Suspension losses' were also mentioned above - energy lost to bike and rider being moved vertically by surface irregularities - and wider softer tires generally save you a few watts of this type.