It is government regulations and legal prohibitions that have created a situation in which there is no competition. The market didn't create that situation, the government did. It is no surprise the price goes up in a market where competition is effectively prohibited.
There are a few solutions: * adjust the regulatory framework to allow competition to emerge * strengthen the regulatory framework and set a price by law * apply public pressure against the sole provider into modifying their pricing
The last one is arguably the 'market' at work. The first two are just doubling down on a regulatory framework.
In any case, 'regulatory failure' seems like a much better description of the situation than 'market failure'.