Multiple sets of wires going to every building is feasible and perhaps even reasonable when we're talking about an apartment building. But digging multiple trenches along suburban and rural roads and driveways leading to single-family homes is very wasteful. It's usually prohibitively expensive for the second company that wants to come into town, and is basically guaranteed to be a negative ROI for the third company that tries to lay fiber to customers who already have two incumbent options.
In the US, Google Fiber has had limited success entering a handful of carefully-picked markets where the incumbent options are rotting copper POTS wires vs coax that can only compete on downstream bandwidth. In some of those markets, the incumbent phone companies have replaced some of their copper with fiber, but a third residential fiber option is still unheard-of. That may not fit the strictest definition of natural monopoly, but it's pretty close: in areas where both Google Fiber and eg. AT&T fiber are competing against coax, it would not be surprising to see one of the two fiber ISPs give up. We've already seen Google give up on bundling TV service, and both Google and AT&T are very reserved about further expansions.