We may be at cross purposes: I thought you were referring to some arrangement as depicted in Velopeur’s picture, albeit with a single piston in the cylinder, but piston rods at both ends. Yes, there is power applied in both directions of the piston stroke, but there is a limit to the amount of power being transmitted, whether it is conveyed to the wheels by a single piston rod, or by double ended rods, due to physical laws.As with coupled wheels versus single drivers, the amount of power transmitted by the piston in the cylinder through the piston rod is fixed by pressure, area, volume, etc, but the reason for having more wheels connected to each other is not to increase the power output (you can’t) but to improve the number of contact points with the rail, increasing the total adhesion and decreasing the risk of slipping (and of breaking rails due to axle loads). If you look at the formula for calculating tractive effort, there is no reference made to number of wheels.
Partly that, but a flywheel also serves to smooth out the pulses from a single cylinder, and to help prevent the piston stopping dead centre (why we have “quartering” with two or more cylinders) by keeping things ticking over: traction engines usually have a clutch early on in the transmission chain, so that the drive is disconnected from the cylinder, along with using gears to change direction. The energy stored in the big flywheel is sufficient to overcome any “stiction” when starting, otherwise the traction engine would stall - and stick on dead centre - whenever a load was applied.I am not sure I would call single cylinder traction engines fitted with a big flywheel “crude”, though. They are actually quite sophisticated solutions to the problems inherent in single-cylinder double-acting piston engines.