I disagree, from experience. I live in an urban environment in the UK with extensive public transport and haven't had a car for the last 5 years.

I have friends and family who live in the 'burbs. There are plenty of times I take a taxi over public transport, including:

    1. I'm in a rush
    2. I need to transport something not small
    3. I'm feeling lazy

Note, that all public transport suffers from some fundamental problems (at the moment[1]). I live in the south of the city. For anywhere I want to travel to in the north I have to walk 10 minutes to get to the bus stop. In certain hours buses get out of sync with their timetables, so you can add another 10/15 minutes of waiting.

Also a lot of public transport has moved to the "hub" model, where you have a central hub which connects different routes. While perhaps more efficient in some ways, it's incredibly inefficient for the traveller. It adds a minimum of 20 minutes to any journey where you have to go through a hub. My sister used to joke it takes an hour and 20 minutes to visit a friend living on a different tube line in London. My home town is either 3 lines switches away, adding an hour and a half of waiting to a journey, or I go through the London Hub, inexplicably having to pay a premium.

So while I like and appreciate our public transport, it can be a huge timesink and when you don't want to pay the "time tax" of public transport, taxis fill the role.

[1]I say at the moment as we can imagine a point in the future where you request public transport with your phone and it can on-the-fly accommodate you.