Hi, not sure how expensive taxis are where you are living, but they are at least very cheap here compared to Europe and especially the UK. Public transport is even cheaper, but it depends on where you live as to which will be best for convenience. I live in the mid levels and almost never take public transport with the baby - taxi is just easier.
Yes, the taxi drivers go fast and can be crazy drivers (I would not limit to just taxi drivers here..) but at least typical journey's / distances in HK are quite short. It's as MLBW says, it's what you are used to. Driving in Italy and Paris - very similar! Otherwise, yes HK taxis may be a harrowing experience..
if you have a younger baby with a stroller / maxi cosi then getting those strapped into and out of taxis is not bad and the safe option. On occaision, some taxi belts are not quite long enough to work properly with a maxi cosi so you need to improvise.
Starting off from your home is generally fine as you can take you time to get sorted and get the baby in etc.
Most importantly you will eventually develop strategies for getting to different places e.g. getting out at nice hotels as the bellmen are always happy to help you in/out and find a taxi, getting dropped off places where lifts are close to avoid stairs.
Once bub is bigger it get's more tricky. Not absoutely ideal, but you can wear the baby in a bjorn/baby carrier and put the safety belt between you and the baby for some degree of protection (never around you and the baby together - this is more dangerous than not wearing one at all).
My baby is a year and although really too big for the bjorn, I can still get her into it for taxis. Always prefer to use our car and a proper car seat where possible, but as only my husband drives when it's her and I, or the helper, we still have to taxi.
There are other options online for portable car seats for older children, I will need to look into this soon I think.
HK is not brilliant for prams, but once you are used to it things become second nature. There are so many other great things about having kids here (plentiful, cost effective help etc.) that outweigh. Sadly air quality is not one of them!
Second Lucylou on the Maclaren, we have a bugaboo which lives in the car and is great for long walks (of which there are many in HK), the beach and and if she will be in the pram for a long time. I have a Maclaren Quest that I use when I'm on my own in town or taxis as it's easier to put up/down with one hand. The bjorn allows me to get out of the taxi wearing the baby and then get/open the pram up.