I don't doubt that my made up example would be difficult to actually pull off in practice, although who knows. There may be enough women who are turned off by the meat market aspect of other dating sites that a service with a zero tolerance for weird behavior might find it appealing. And both sexes may find the idea that "the system" automatically weeds out inactive or unsuccessful daters appealing, knowing that they will be much less likely to waste time on "losers".
I think there are some "higher end" in-person dating services that cater to higher-income professionals looking for long-term relationships that have made something similar work. They cost a bundle and involve a lot of human interaction and these kinds may be doing the sort of active filtering that eliminates dead wood.
I also wonder if the pricing model of dating sites isn't skewed against more and better matches. If women (or even men) gain access at reduced costs, they may value it less and invest less in it personally. If men pay a higher cost for access, they may over-engage because they value it more than women and appear desperate when really they're just trying to get their money's worth.
I suspect that some minimal level of cost to participate is probably necessary -- without "skin in the game" it's too easy for people to willfully not participate and create imbalances in interest. You probably could also benefit from a "participation economy" -- credits against your bill for responding to messages, credits for going on any kind of a date, etc, with credits valuable and easy enough to obtain that people who are actively engaged in the site might actually end up having zero monthly cost. Encourage participation, discourage non-participation.
I'd also wager that some kind of moderation system would make sense -- I hear a lot of complaints from women who have used online dating that the creep factor is really high -- men who make lewd propositions to people whose profiles are listed as "seeking a relationship", etc. Perhaps users bothered by a message could submit it for moderation, and moderated messages would be anonymously displayed to other users who could vote them up or down and receive credits for it. I would probably limit moderation of messages to people seeking similar relationships, since those looking for longer term relationships would have a lower tolerance for messages suggestive of casual encounters. This would avoid an obvious values conflict between the two groups.
Users who have messages moderated as inappropriate would lose credits. Users who submit messages for moderation where their complaints are unsustained would also lose credits. This would enforce a kind of community standard for acceptable behavior as well as discourage people from being offended too casually, and I think the latter is probably equally important. I think there are people who are single not because they don't want to be in relationships but have really skewed, intolerant or unrealistic standards and are basically single because of it.