I'm wondering how those of you who advocate asking the woman's partner would deal with the situation of the partner being unhappy that his date dances with others, but she wants to? Is your rule about showing respect to the other guy going to superceed her desire to dance with you if you asked her? Is it your place to "respect" him when she is trying to simply go about her business developing her tango, rather than be controlled by his jealousy?
Sometimes my boyfriend and I are at a milonga where there are very few followers he would want to dance with, or he simply is too tired, and does not want to be social. So that night I do not circulate either, even though there are guys I would like to dance with, and I know they are willing to dance with me. Usually people around are sensible to that kind of situation, and accept that. I know my SO will be pissed off if somebody ( a leader or a follower ) chose to disrespect that situation, and insist on asking either one of us.
I do not mind. I know there will be plenty of time to circulate and "develop my tango", as we both normally love to do exactly that, and dance with other people.
My point of view, there is no "independent". We have to consider our partner's feelings, consider existing relationships, and work things out the best we can. The traditional tango etiquette was created for that purpose, too.