I don't think you need seat suspension for bicycles to beat walking. On the kinds of surfaces that foot traffic naturally forms, am average commuter bike is gonna perform very decently.
I think the only qualitative difference would be that modern roads are usable all year whereas natural tracks are generally gonna get unusable when it rains a lot.
It's incredible that we have machines that can take that kind of a beating, while also having precision components on them, and also being light enough to pick up in 1 hand, and being affordable to the poorest members of society.