Regardless of reputation or how good a hospital is for most matters, if they don't understand thalassemia, you won't get proper answers. A doctor telling you that you do not need to know if you are a thalassemia carrier is being highly irresponsible. Every carrier on earth should know so they can make truly informed decisions about who they have children with and what precautions if any, will need to be taken to prevent a tragedy like hydrops fetalis, when a baby is missing all four alpha globin genes and can make no usable hemoglobin, resulting in death before or at birth. When two alpha thal traits who both have two gene deletion alpha thal have a child, there is a great possibility that their child will have 3 or even 4 alpha globin genes deleted. If all four are deleted, the result is hydrops fetalis and the baby dies. In the case of three gene deletion, the child may be transfusion dependent for life. These are things every parent has a right to know and would want to know before making a choice about children. I don't see how any doctor can tell a patient that they don't need this information. In the US, patients do have some protection under the Patient Bill of Rights, and one of these rights is a right to be informed about all aspects of their medical condition and all treatment alternatives. If you request testing, there should be only compliance from your medical providers. And you are very correct. There is no reason your child would ever be excluded from insurance because he carries alpha thal trait. It is a mostly benign condition and his medical needs will not be much different from anyone else.
One of the big roles I try to take on is one that promotes education and awareness about thalassemia and one of the reasons is so that prospective parents can make informed choices when deciding to have children. Without testing, this is not possible. Even though carrier status may not lead to any major health issues in carriers, they do need to know for the sake of future generations and their own sake as parents. Even when parents consciously make a choice to have a child in spite of the risks, and have a thal major child, it should be their informed choice and not done out of ignorance.
Other than folic acid, there is very little one can do even when it is three gene deletion alpha thal. Strengthening and protecting the immune system is important. A multivitamin is a good idea. I would also recommend watching the developments in the research into Fermented Papaya Preparation, as it has been shown to have a positive effect on the immune system. If it turns out your child gets sick or infections easily, it may be something to consider. Working to stay healthy is the best treatment for alpha thal. Alpha trait may result in very little in terms of problems, so now it's important to just maintain normal health.
I would not hesitate to recommend testing to anyone who may be a carrier of any blood disorder. Testing can prevent so much grief later on. The law says that you cannot be excluded from insurance and that insurance is portable, which means that when you change policies, you cannot be excluded from coverage on something you were insured for in your last policy. I don't think this is where the threat to insurance will come from in the US. The real threat is the elimination of employer provided insurance, as one of our candidates for president wishes to do by taxing employee's insurance benefits, removing the tax exemption for employers who do provide health insurance and then giving workers a tax credit too small to cover their insurance costs. This is a horrible idea and will lead to tens of millions of people losing insurance if it was ever to be put into law. We do have protections but if we can't afford insurance, the protections won't help.