Lack of competition is not the root cause. It's all the regulations. Certifying a new GA airplane takes a lot of time, and costs a fortune. This translates to high development costs, and certification costs, and ALSO is a huge barrier to entry for new companies, and a significant barrier for existing companies to develop new modern designs.
I could potentially muster enough resources to design and build an ultralight aircraft (that does not need any certifications), but a type-certified aircraft even as simple as a Cessna 152? Forget about it.
You could argue whether those certifications are worth it for safety, e.g. by comparing Canada's much more generous ultralight aircraft max weight allowance compared to US, or looking at the change in accident rates in European countries that recently deregulated ultralight aircraft, but whether it's worth it or not, regulation is the single most impactful market force driving the cost of GA aircraft.
Lack of competition is also sometimes directly enforced by the government. For example, several countries mandate the use of FLARM, a proprietary collision avoidance system for light aircraft. Governments gave this company a monopoly without requiring their protocol to be made interoperable, open source, and dis-encumbered from patents.