LordKenmore - you're totally right about that! I didn't think of the clock! The old Telechron-style clocks did indeed time by using a synchronous motor linked to power frequency. Would be running quite slow if designed for 60 Hz and run on 50.
As far as volts and amps and which system supplies what... Loads like a stove, dryer, or central HVAC system have a dedicated circuit with whatever breaker is recommended for the end device. A 50A for a stove for instance. These for the larger appliances. Since this discussion was about a large free-standing range, that's what I am going to be focused on.
For outlets; in USA, we have multiple branch circuits for our regular, every day wall outlets. They often have rated 15A outlets with a 20A circuit breaker supplying 3 or 4 outlets. A house may have many of these, 10 or 20 or more 120V branch circuits. The outlets provide whatever the appliance plugged in demands, and as long as the total on that circuit does not exceed 20 amps, there is not a trip.
In other parts of the world, they often have a ring-main configuration, with a single breaker powering many outlets. The appliance power cords themselves each have their own own fuse or overcurrent protection.
These are two different ways of accomplishing similar things. The differences are in where the complexity lies and where the costs are located in the system.
You can't say that the UK system has half the amps as the USA system. Both provide what the connected appliance demands, until an overcurrent device trips. In the US system, that is a breaker in the panel whereas in the UK it should be the fuse in the appliance cord its self.
The center-tapped neutral of the USA system is in place to reduce the voltage potential from phase to earth ground. This will reduce the level of injury caused in a typical electric shock accident. People are injured by the amount of current which flows through the body, and the path it takes through the body. A confined current path from one finger to another because you touched the outlet terminals while plugging it in will not kill you. A current path from a hand, through the body, to a foot or the other hand can indeed kill. These dangerous shock paths are likely to result by one hand's contact with one part of a circuit, and another body part touching earth ground. The center-tapped system reduces by half, the potential from a live conductor to ground. The amount of amps which flow through a person's body is determined by two things: The voltage applied, and the resistance of the body. Body resistance varies widely; based on what (if any) clothing or shoes are in the ground contact path; and how dry your skin is. That can't be predicted. But Ohm's law states that current is equal to voltage divided by resistance. I=(V/R). So if you cut the voltage in half, for any given conditions you would cut the shock current by half. There is another effect which has to be taken into consideration. The human body has a thin dry layer of skin which protects against low voltages, to some degree. Below about 50V on unbroken skin, you will not receive a dangerous shock. Above 50V things go badly because the dry outer layer of skin may break down and allow the current to break through to the wet (and very conductive) layers underneath. This happens suddenly and, again, can't be predicted. When it happens, a mild shock suddenly turns into a major electrocution. The higher the voltage potential between the conductor and ground, the greater the chance of this happening.
So, the conclusion is, the more complex center-tapped system in US was envisioned to help save lives. It limits the level of injury in event of an accidental contact with a live conductor. This was developed before the concept of GFCI or RCD systems were possible and we still use it.