If I'm cold calling someone for money and mentorship I feel like the pressure should be on me, honestly. At this point I'm the only one with something to prove, the angel has the luxury of being as picky as he or she wants to be.
I disagree. Investment is a two way street. Angels benefit from deal flow as well so making themselves unavailable does seem odd. If they want to invest in early stage ventures but don't have the time there are plenty of other vehicles to put their money in without being bothered