For liability, yes if you are involved in a plane crash with a high dollar value lawsuit then it probably won't matter (unless you can convince the court that it is a separate business leasing entity). They are going to look up LLC and start researching it). LLCs do provide ability protection however (it's in the acronym!). It can create a firewall between assets. In some states even if you have a charging order you cannot force an LLC to disburse assets.
You can be sued for literally anything. Defamation of character, slips on your property, and minor car accidents. Having your assets segregated, complex, and difficult to locate will help you and can even prevent frivilous lawsuits. Ideally you own nothing and are a pauper on paper... no planes, real estate, stocks, bonds, vehicles, etc. You want to control assets, not actually own them personally. If assets are in your name, they are much easier to locate(simple 60 second search) and collect with a judgement.
Many states allow you to form an LLC and have no sales tax. You can buy the plane in an LLC and potentially not pay sales tax, but it depends regarding state law where you reside and if you plan to bring that plane to your home state. Many people are already doing this to buy supercars, saving tens of thousands of dollars in sales tax.