Courts in a variety of states have “pierced the veil” of a single-member LLC from the outside and have held that it is not a separate entity and thus may not be used to protect the assets of the LLC from the creditors of the member.
You get liability protection, yes, but not as much as you would if you had one more member. The veil can be pierced for various reasons, so to reduce risk you want to minimize those reasons as much as possible.