Does flywheel weight matter on a spin bike?

Reviewers generally treat a heavier flywheel (around 35-40 lb) as a proxy for a smoother, more stable pedal stroke. garagegymreviews.com flagged the NordicTrack T Series 9's 19-pound flywheel as a source of side-to-side wobble, while the Schwinn IC's 40-pound flywheel was repeatedly praised for smoothness. That said, magnetic-resistance feel matters as much as raw weight.