The Dangers of Travel
While we tend to bemoan how dangerous cars are nowadays, traveling by coach had a lot more issues. Getting into a coach was no guarantee that you'd get there safely for a number of different reasons.
First off, there were two terms for robbers: highwaymen and footpads. The first robbed on horseback, while the second did so on foot; carriages often had to stop for various reasons, and the footpads could simply walk up with a pistol and rob them -- or stand in the middle of the road and make the horses stop. We tend to think of footpads as only robbing pedestrians, but they were known to "carjack" as well. In fact, because horses were expensive to own and maintain, footpads were more common than highwaymen.
While it's popular in modern depictions of the 1800s to show poor travelers being assaulted by highwaymen every other day, in reality, the Regency era didn't have a huge problem with such crimes. In the early to mid-1700s, it was a serious problem, but between travelers protecting themselves, high bounties on robbers, and a serious legal crackdown on offenders, the problem was mostly eradicated by the 19th century.
According to "Coaching, with Anecdotes of the Road," Lord Lennox states that robberies continued until about 1814, which was the last account of a stagecoach being robbed. However, even before that, it wasn't a common problem. He states that in all the time he spent traveling (and he did a lot of it), he was only robbed twice. So, it was not a common issue by the Regency era.
The crazy thing is that robberies didn't happen just on long-distance trips. Lord Lennox also stated that most carriage robberies happened on the streets of London. You were much more likely to be robbed during your afternoon ride through Hyde Park than on the highways. Of course, the demand for better public safety led to the government stepping in and going after the problem, eradicating it first in the big cities and then in the countryside.
Carriages were way more dangerous to drive than cars. Between the fact that they were top-heavy and difficult to maneuver, horses can be dangerous and unpredictable. In the 1860s, an average of four people were killed by horses and carriages every week in London. To put that into perspective, modern London has roughly thirteen times more vehicles on the road than all of Great Britain had at that time, yet they only average two and a half vehicular deaths per week. So, yeah. Carriages weren't safe.
One common issue was the fact that many people simply didn't know how to drive them properly. Lord Lennox doesn't give a very sterling recommendation for coachmen in his time. Throughout his book, he paints most stagecoach drivers as drunk and unscrupulous men.
For example, the opening of my book, Honor and Redemption, was directly influenced by Lord Lennox's accounts. He said that most young men learned how to drive on stagecoaches during trips to and from school. Driving was very popular and driving a "four-in-hand" (or a team of horses) was considered the peak of coolness for the young gentry, but it wasn't easy to get the opportunity to practice. A lot of the young men didn't have access to a carriage and team or their families weren't stupid enough to allow them to use their private vehicles to learn. So, the young men bribed the coachman to hand over the reins. Of course, the kids didn't have a clue what they were doing and handling four horses at one time is not an easy thing. Driving a carriage isn't like driving a car -- unless your car has four engines that all have minds of their own and a tendency to get spooked. Not to mention that stagecoaches were extraordinarily top-heavy with upwards of twelve people up top (and a mountain of luggage), making them easy to tip over. Needless to say, this led to a lot of accidents on the highways.
It makes me think that if a family had a professional coachman on staff, they would have to be a very trusted servant. You are literally putting yourself and your family's safety in his hands, trusting him to keep your coaches and horses in good repair and handle them responsibly. During this time, there was no regulation controlling the training of drivers or who could drive carriages.
But even if it wasn't pure idiocy or carelessness on the driver's part that caused accidents, carriages weren't safe to ride in. Governess carts were introduced in the early 1900s as a safer alternative to the more popular dogcart, which was a popular family vehicle and also had a bad reputation for children falling out of them; imagine driving along and having your kid simply fall out of your car.
Many of the carriages also had a high center of gravity (especially the two-wheeled kinds), making them easy to tip. Well-trained horses can be very reliable, but a horse is still a horse and can be spooked, which could make you crash. Road conditions were terrible, leading to carriages slipping off the road and tipping.
All in all, not a great recipe for safe traveling.