300,000km is about 186,000 miles...
In my experience with higher mileage cars is that the engine itself (meaning the block, camshafts, crankshaft, pistons, valves) didn't need repair at that mileage, but rather, some of the other components began to fail. Your alternator replacement is a good example.... Others that I've seen include water pump, fuel pump, radiator, CV joints, air conditioner compressor, and voltage regulator (sometimes this is integrated into the alternator).
That's been my general experience with higher mileage vehicles in general, not limited to only the Corolla.