It's hard to see but on the overhead power lines, houses seem to only be grabbing one phase of the 3-wire transmission line. If each house is using a separate phase, what makes the 3-phase system an advantage if each house still has the 0-voltage point of the sine wave?
Generally (in the US, anyway), several houses in a neighborhood will all be supplied by a common pole transformer, which will be attached to a single phase of the medium voltage (several to tens of kV) distribution network. Each house is connected to the center-tapped ("split phase") secondary, giving 120V-0-120V, or 240V across the ends, at anywhere from 100 to 200 amps max.
It's possible that all three phases of the medium voltage network are wired along the street, and the pole transformers will alternate among the phases, but I've seen quite a few areas in which all the pole transformers on an entire street or neighborhood are all on the same phase, and different streets are on different phases. In either case, the three-phase load that the power company sees balances out statistically, rather than rigorously.
While 30 or 40 years ago it was common to get 3-phase power in many European countries, today as a rule you get one phase. If you get the R phase, your next door neighbor will get the S phase, and the person in the house next to that will get the T phase. Over hundreds of houses this more or less balances the three phases. 3-phase power is still available at an extra cost, but households hardly ever need it anymore. (I remember my mother had a Miele washing machine which ran on 3-phase power.)
Industrial customers often will have 3-phase power, either because they need lots of power, or they use machines which run on 3-phase power, like synchronous motors. Overall the three phases coming from a 10kV transformer station will be fairly balanced, with only a small residual current through the neutral.
Different houses will connect to different phases so that they hopefully load them equally. Of course that's not possible at all times but even in the worst case scenario when all the consumers are on the same phase the current in the neutral will be equal to that in the used phase. So the system still allows you to use four wires instead of six and that's significant saving of wires.