Well, the beauty of the common law tradition is you, as a hypothetical co-habitator, have no idea whether you are "accidentally married" in any particular regar

Well, the beauty of the common law tradition is you, as a hypothetical co-habitator, have no idea whether you are "accidentally married" in any particular regard unless or until the matter comes before a judge for whatever reason. Your aggrieved former not-quite-spouse can make whatever claim to equitable judgement that they can imagine in, say, Colorado. Contrast this with, say, Poland or France, where under their civil traditions there is no chance whatsoever that your unmarried person who lived with you will be able to claim your estate when you have died.