For those who can't be bothered to read the long post: Reliability of model in question plays a big part, some cars are hardier than others. But yes, regular servicing and prompt replacement of failing parts and those parts related will ensure long life. In fact, many vehicles in Singapore can hardly be called old or high mileage.
I drove taxis in Hong Kong for slightly over a year in 2011-2012, and remember driving one which had clocked 700k km. It didn't feel any worse than many of the others that had clocked 300-400k; in fact, it was well-maintained and the acceleration was pleasantly nippy. Until today, I still see that taxi near my place and the regular driver washes it at a certain time every evening as long as it isn't raining.
Asked the head mechanic from the company I rented the vehicle from if the engine had been overhauled, but it hadn't! Basically, he told me the same thing - frequent servicing and immediate replacement of any parts if necessary. In fact, they used cheap mineral oil, but that was changed every 2 - 3 weeks with the kind of mileage most drivers clocked. Automatic transmission fluid was apparently changed every 2 - 3 months - the head mechanic did not want to risk gearbox failure as many of the drivers have the bad habit of coasting in neutral, something carried over from the past manual days. Tyres were changed the moment they started to lose thread, something like once every 3-4 months.
In that period of time, I drove more than 20 of those taxis, 3 to 4 times a week. But despite the fact that none were newer than 8 years old and many older than 10, and also that I beat the hell out of them whenever my cab was empty, I never encountered any mechanical issues (apart from aging suspension parts at times, which were promptly replaced once I highlighted to the company). It's been at least 6 years since then, but I still see most of the taxis I drove plying in my neighbourhood today. Many of them are 14 - 17 years old today, and I never fail to be amazed by how sprightly they feel.