Suspension bridge oscillations were a well known problem long before the Tacoma Narrows disaster. The Brooklyn bridge has a system of diagonal cables from the roadway up to the towers to control oscillations.
As David McCullouch notes in his book o the building of the bridge, both John and George Roebling, the father and son team of designers and builders, realized the importance of keeping the bridge itself heavy and stiff, and built it that way. even without the extensive series of diagonal cables, the bridge would probably resist those sorts of oscillations.
A friend and I walked over a very small suspension bridge for pedestrians, whose main span was probably about 40 feet and whose cables were small enough to wrap your hand around. We noticed it bouncing with our walking cadence, and so we positioned ourselves at about the 1/4 and 3/4 points and started jumping up and down out of phase, and really got it going. So, I can attest that suspension bridge self-resonance isn’t difficult at all to just notice while on a walk.
Nitpick; John and Washington Roebling.