I think they do it for a few reasons - some good - some less so - many "street" preachers are also homeless and have mental problems. The ones going to door-to-door are kind of "forced" to do that by their religion - it is part of the requirements to join the church. Many do it because their interpretation of "witnessing the gospel" includes preaching the word to others.
But a lot of people who believe really have gone through a life-changing event and usually for the better. Sometimes they were criminals of one sort or another, terribly unhappy or just empty and they found Jesus (or some other religious figure) and their life really turned around. They made a lot of new friends that care about them and it makes the tough times a lot easier to lean on Jesus so they want to share that joy, happiness and fulfillment with you. They see and know the positive changes that they experienced and i think out of kindness want everyone to know this kind of completeness.
Keep in mind this is coming from an atheist who would, when in a bad mood, eradicate religion if he could.
And while I appreciate your commitment to disbelief, again as an atheist, I will say straight out there are quite a few things that would make me believe. A real honest-to-god miracle for example - or even something more subtle. I don't know if you've read the book Contact (the movie doesn't do it justice) but the part where they are solving PI out to some incredible amount of digits, when placed in geometric shape the digits spelled out a code that couldn't have come from chance (or something like that - now I'm not doing it justice) the point being - it was god's signature - or according to Sagan - the signature of the prime cause or something like that - keep in mind Sagan was an atheist also. That would be another bit of evidence that would sway my belief towards the "higher power" side of things.
my two cents anyway...