It seems to me like it might be a good idea to require citizenship to create an LLC.
For what it's worth, the formation of an LLC is a state affair, and every state has its own rules around requirements, reporting, transparency, etc. Most states keep the paperwork public; some states don't, but these are not the states where housing shortages are all that profound.
If this hypothetical low income person owned the LLC so that others could operate it, nothing is stopping them from cleaning out the LLC's bank account whenever they want since they own it!