Sure you have the right to contest the claim, but it's you, John Q. Nobody vs. person who does this for a living. How many people out of 100 can present an organized, convincing case on their own that will rival an "industry expert" without hiring a lawyer? Not many, with BenK being one clear exception. Most will need a lawyer, simple as that.
The most a judge is going to award you is enough to make you "whole," then the lawyer is going to take 35-40% of that. In most cases the lowball settlement is comparable to what you'd end up with in this scenario, and the adjusters know this. So it's a question of take the money, or subject yourself to the lawyer and all the associated headaches, and end up with the same money.