The purpose of a thermal overload is mainly to save an expensive, high horsepower motor. A typical failure would be a bearing. A motor will start drawing more current with a bad bearing. With fuses or a breaker, there's a good chance the bearing would go to total failure, tearing up the shaft, housing, or even burning up the motor before the breaker trips. A thermal overload is much more sensitive, tripping as soon as current draw goes up just a few percentage points.
For pumps, the thermal overload minimizes damage possibly allowing a rebuild.
With a cheap motor, we don't care. If a bearing fails, we're going to throw it away anyway. Also, with something this small, a fuse or breaker most likely will trip before total failure. Fused at 1 amp, it would probably draw 2 Amps or more with a bad bearing.
A 50 HP motor might be fused at 80 Amps, draw about 60 Amps full load, and maybe 65 amps with a bad bearing.