Taxi with Baby in NYC or Not to Taxi? A Parenting Dilemma

UPDATE Oct. 2016: In addition to what we talk about in this article, a newer option for getting around with your child is Uber Family’s car seat service. Click the link for more info.
I was running late to my 10-month-old’s gym class downtown. I was faced with the new parent dilemma — do I take a risk and hop in a New York City taxi cab or go on public transportation and be extremely late to the class.
I decided to take an NYC taxi with the baby in tow — something I have done less than five times with my son during his brief life because I know it is unsafe. I am told that the New York State law requiring infants to be in a car seat while riding in a car does NOT apply to taxi cabs. If that ‘hearsay’ is true, I am not sure why cabs are exempt from that particular law. Anyhow, we arrived at our gym class safely and on time. However, it begs the question: What is the safest way a parent can transport their child in an NYC taxi cab?
To be honest, I rarely see anyone carry around a car seat in NYC. On the other hand, I know it is not safe for babies and toddlers to ride on their parents’ laps in taxis while they barrel down the streets. Someone told me that when in a cab, they put their baby in a Baby Bjorn, and seat belt them both in because it is safer – is it really? I also learned that there is a lightweight (approx. 4 pounds) portable car seat that fits into a bag. It’s not as secure as a regular car seat, but I suppose it is better than nothing.
Sure, taking the public bus or subway is a safer and less expensive way to travel. Please help me and other NYC parents …
What do most people with kids do in NYC when they need to take a taxi with a baby in tow?