It can be! If you've got a crack legal team at your disposal, you can absolutely sue over insurance denials that put your health at risk. The problem is that most folks who need an insurance plan that regularly denies them also don't have the money to afford a crack legal team to sue the insurer. (If you're that wealthy, typically you would just have a private physician that you're paying directly, who has no problems treating you promptly because that's what they're paid to do.)

This is representative of a general problem with the legal system today. It's too expensive, and operates too slowly. When the economics of cheating people were that you might be able to cheat 10 people before you pick on the wrong guy who has a lawyer that puts you out of business, you have an incentive to follow through on your contracts and do what you say you'll do. When the economics became that you can cheat 10 million people before you pick on the wrong guy who sues you, it becomes rational to take the money from those 10M people and use it to outspend the guy who sues you, or at least just pay him off so he goes away. And so our western notions of democracy and contract law get subsumed into a feudal system where only big corporations get protection of law, and you must join the local protection racket to slot into that system.

The problem is that when such things happens, insurers have said - and won - in Court with:

"We are not denying or delaying care for our customer. We are, instead, only noting that we are not going to be the Responsible Party for paying for it. They are, as they have been all along, free to get the care they believe they need and pay for it themselves."