And yet, nobody says the possibility of their sister dying and leaving them with three unexpected kids is a good reason for cars to be issued to people by the government based on what car experts decide they need. In most areas of life people are expected to decide how much risk they can stand to bear, make their own decisions of how much to pay to mitigate it, and eat the costs themselves if it turns out they didn't take enough precautions.
And yet, almost everyone accepts that it's a good thing for the government to set a minimum skill level and to issue licenses (without which citizens may not drive unsupervised), that depend on demonstrating that they meet that minimum skill level, both prior to being issued a license, and on an ongoing basis whereby repeated and/or severe misbehaviour may result in the withdrawal of the license.
I don't care if you can afford to compensate me if you kill my sister; I still don't want you behind the wheel if that's a foreseeable consequence of your ineptitude as a driver.
The government is right to be able to define not only whether you can operate a vehicle on public roads, but also to define what broad categories of vehicle you may operate - you need a different class of license to drive a vehicle above a certain mass, or size, for example.
The decision about which light vehicle you use is yours; The government doesn't mandate whether you drive a Smart FourTwo or a Ford F-series ute, but they do get to say whether or not you're fit to drive at all, and they do get to limit you to light vehicles unless and until you meet the higher standards required to demonstrate your ability to safely operate heavy trucks, buses, and other specialist vehicles; And to require special licenses for certain use cases - for example, you can give your friends a lift to town, but if you start running a business transporting people around, you're likely going to need further licensing above and beyond your standard drivers license.
The details, of course, vary depending of your jurisdiction.
But the principle is certainly widespread that the government can, should, and does dictate to people what vehicles they can and cannot drive; But that the details of the choice is left to the consumer, as long as they choose within the specifications of their licences.
The consumer gets to choose what car he drives, but if he wants to literally drive the bus, he needs special permission from the government.
In my jurisdiction, that's in the form of two separate licenses above and beyond the standard driver's licence: one to operate heavy vehicles (those with a GVM greater than 4.5 tonnes); and the other to carry more than 12 people and/or to carry passengers for "hire or reward" - ie to operate a part of a business. (note that if you want to carry more than 12 people in Queensland you need a Driver Authorisation
even if you are driving a light vehicle and are not being paid to do so.) The "DA" certifies that you are medically fit and requires you to pass a stringent medical examination at least every five years, and every year if you are over sixty years of age; You also need to pass a criminal record check to obtain one, and to have a good traffic violations history. If you've ever been fined for DUI, or if you've been fined for speeding or red light violations more than once in the previous five years, you can forget about getting one. They're a lot easier to lose for violations than a driver's licence, too.
TL;DR: Oh yes they do. Just in a fairly limited way.
Which is the whole point of a mixed system. Neither extreme would be better than the mixed system.