Isn't supplying three phase power to regular retail customers UNSTABLE?
In the USA, a small block shares a 240V split-phase transformer.  The primary of that transformer is on typically 2400 volt 3-phase delta, one leg obviously.   The next block over is tapped off different phases.  
In Europe, a neighborhood gets a 415V 3-phase wye transformer, and the first house is connected to phase A and neutral, next house to B and neutral, next house to C and neutral, etc.  Some houses get 2 or 3 phases, particularly if they are load-heavy.  It's as simple as delivering one more wire.  They can then connect appliances to 415V, but that is rare except for serious tradesmen or hobbyists with industrial tools.  
In Manhattan, a block gets 208V 3-phase wye, house 1 gets phase A and B and neutral, house 2 gets B, C and neutral, house 3 gets A and C etc.  
Distant rural America often sees ~10kv single-phase with a transformer at each farmhouse. However this is one side of 3-phase delta, the next farm road will be tapped on the next phase.   
Australia sometimes distributes at high voltage with a single wire and earth as neutral, literally one solitary wire on the pole.  It is 3-phase "wye" with the other 2 phases going down other distribution lines.


All distribution is 3-phase - if not to the pole, at least to the neighborhood.  

So what choice do you have? Nobody is seriously going to run a big single-phase distribution system**, and do a large conversion from 3-phase to 1-phase, simply over imbalance. 

It averages out

Imbalances aren't as big a deal as you might think.  With a sufficiently large number of houses to average over, eventually load per phase averages out.  

If for some reason it doesn't, the power company can change which phase a particular flat or block is tapping.  

Now if the town's large industry decides to heavily load one phase and create an imbalance, then they might get a serious talking-to by the power company.  Because they are big enough to create an imbalance too big to average out.  



** Except the railroad.  Look on Amtrak's Northeast Corridor, see the even number of power lines?  Single phase.  They have to solve the "how do you put an enormous single-phase load on 3-phase" problem.