"you suggest people waste: - a lot of their own time" I wouldn't call it "wasting time" if it gets you the result you want.
"even though you have nothing in common with them" Being startup founders is already having a lot in common.
"All you want is a backhanded intro" I wouldn't do any of this in a backhanded way, founders will smell it. Be transparent and upfront.
"Only so that the investor will get 2-3 emails" The question was how to get warm introductions... these are warm introductions :)
"from founders who really know nothing about you other than what they found out in a 10 minute phone call" ... or from follow up interactions you've had with them after that initial 10 minute phone call...
"Don't you think that system is broken?" Nope :) I think it's an imperfect system - but then everything in the real world is.