Even,
"...2:30-3:00pm and it's p!ssing down as usual..... now try to get a cab to take you to Jurong.
The problem is, let's say.... i take the little one to school, have a breakfast appointment with a client, need to go to the bank, get back to the office to tidy up some stuff then have a sales or service visit in Pasir Panjang, Tuas or Sembawang..."
1. You are using an extreme situation to justify an irrational purchase (a car). It's kind of like Americans who live in urban areas purchasing SUVs..."just in case it snows really hard one day"

2. Most residents don't own a car here and somehow they get on happily, even in situations more extreme than the one you describe above
3. Taxis are not as scarce as you state
"...Few people live above an MRT/Bus Interchange..."
You don't have to live directly above major transport links....just close to them - and savvy renters/homeowners do just this
"..., work 9hrs in an office, don't need to go anywhere else and live completely dull existences. The car takes me everywhere i need to go in a reasonable time, including easily over to Malaysia, and I can get far more accomplished in a single day..."
I disagree. Most residents here don't need to leave the island on a regular basis, and most residents anywhere in the World do live pretty dull existences!!
Even the rare scenario that you have attempted to concoct does not make the purchase and maintenance of car a sensible decision here.