Remain can be used in the context of states. For example, i would like to remain alone. The state is of being alone. Other states could be: happy, free, occupied etc. Remain as, has a similar meaning, but, "remain as (state)" is not correct. You will see "remain as" when the write/speaker wants to give further information. For example, i want to remain as happy as possible. I want to remain free VS i want to remain as a free person. I want to remain american VS i want to remain as an american citizen. There is a subtle difference that is difficult to explain, but 'remain as' will usually be used to give more specificity to the sentence.