I think that for a person to engage in any healthy, close relationship, there's a need for them to be whole and happy by themselves. That condition, in no fashion, precludes any romantic ties, as having a relationship only adds to an enjoyable life.
The converse, that of a situation where a person isn't whole and happy, simply means that getting involved with somebody else means dragging issues along that will work against the relationship.
Citing the experience of monastics isn't going to provide much of an insight on human behavior. Such folks are such a small percentage of the population that they really do stand as outliers in the data. THe human experience encompasses not only those with little affinity for close, intimate relationships (and the monastics may simply substitute religious experience for such), but the rest of the sweep of humanity and the variety of attachment needs. In the same fashion, one can't assume that all humans should be comfortable with upwards of two dozen strong romantic relationships simply because some people are.
As for dating torpedoing happiness? I don't think so. Dating can, perhaps, torpedo self-confidence. Happiness is a more fundamental state, in my experience, and I've been happy (!) to be able to tap into my pool of happiness even when most stressed by events not fully under my control.
When speaking of various forms of non-monogamy...it ain't poly if you're just fucking around.
While polyamory, open relationships, and swinging are all distinctly different approaches to non-monogamy, they are not mutually exlusive. Folks can, and some do, engage in more than one of them at a time--and it's all good.