"Try being an educated, competent single woman of a certain age in the 21st century. Professional men find us intimidating."

I don't. Many of my buddies don't; they seek out women that match that description, with disaster occurring frequently because you're most likely to find ladies like that at work. I think that you are indulging in a stereotype that makes it easier to explain why you haven't found Mr. Right yet. Not that I'm any better, I have my own personal excuses and stereotypes to overcome.
"Do men really want woman who need to be rescued?"

Sort of. Not really. Many men - I venture to say 'most' - like to be needed - it sounds like your sister is playing on this. Wanting to be needed need not mean needing 'Needy', though (*whew*).
"...he moves on to find another more deserving damsel."

It sounds like YOU are attracted to 'needy men' here - men who crave drama. Such men are as common as the women that provide that drama. You seem to be pretty uncommon to me; that you want an uncommon man means that you may wait longer than others. Uncommon men are, well, uncommon.
"Not all woman care about money, cars and travel."

However, no matter how ugly that fact is, many, many women - perhaps even the majority, do find such things attractive. After all, if a man can provide those things, then at least the initial dates are liable to be more fun (to provide a rationale). It's true that you can have fun with nothing, but it takes a lot more 'chemistry' between the two than usual. That too makes such things less common (and perhaps more 'special').