What exactly is it about engineering those rockets that still is so "unsolved" that there are still accidents? What is the "main problem" which apparently is still so difficult to secure?
I would argue that it's money. We know how to make rockets more reliable, it's just that the cost outweighs the benefits
This article Seattle Times quoted the success rate of commercial space launch at 96%. What if we could cut the accident rate in half? i.e. 96% to 98%. There is an obvious benefit there (less rockets blow up), but there is also a cost. Specifically, to make a system like this more reliable, you may need to do one or more of the following
1) Make parts of your rocket structure stronger. This is generally going to add weight. For every 1 pound that you add to the rocket structure, you need to add about 10 pounds of fuel. Further weight tends to snowball. If you add 1 pound to some part to make it stronger, then whatever part supports your first part now has to carry more weight, so it too has to be stronger, etc, etc, and then multiply all of that by 10 to get the added fuel weight. So engineers tend to make things as light as possible, which means occasionally they aren't quite as strong as they should have been.
2) Test more prototypes more rigorously before sending into space with a real payload. This is expensive, because rockets are expensive. This article AirSpaceMagazine quotes one SpaceX launch as $57 million. At that price you can't afford to do 50 or 100 full scale tests with a new prototype before you enter service like you could with a car. E.g. SpaceX Falcon 9 had only 3 full up test flights before they put an actual payload into orbit Wikipedia. Imagine if Ford only drove a new model of car on the road 3 times before selling it. A few accidents or malfunctions here or there would not seem like much of a stretch.
3) Analyze the design more thoroughly. Computers are cheaper than they used to, but they still aren't free and more importantly you have to hire experts to do the simulations (who salaries often run into six figures)
Add all of that up, and you may conclude that an occasional accident is actually cheaper than the alternative.