Most water heaters are built for “quick recovery.” The top thermostat supplies power to the top element until the top thermostat is satisfied. Top thermostat then switches power from the top element to the bottom thermostat which supplies power to the bottom element. This is called non simultaneous operation.
Ohm’s Law for a resistive circuit states that the current is proportional to the voltage. Cut the voltage in half and the current goes to half. Power is the product of voltage times current, so power goes to one fourth. Thus a 4500 watt element at 240 volts produces 1125 watts at 120 volts. Recovery also is 4 times as long. If wiring the water heater at 120 volts, you can wire the thermostats for simultaneous operation. (Don’t bypass the ECO.) This will give you 2250 watts output.
If an element is rated at 4500 watts and you only ask 1125 watts from it, the element will last not indefinitely but a long long time.