The arguments for it have been a'brawling and assaulting, the counter-arguments the campaigning, yet giving somebody those spare coins from your pocket post-your Sainsburys trip is still mostly brushed under the carpet of 'it's your own friggin' business what you do with your money'.
So here are some theoretical, non-common sense rationale for giving away one of those £1 golds you think you might need for the laundry:
1. It's an acknowledgement of human dignity, or loss/lack thereof. Since we're wired to be dignified beings, cf. human pride, when somebody is on the street with their expression downcast and form lifeless, or when they're stroking the back of the ears of their dog and calling out to you and wishing you a nice day but very clearly not having a nice day themselves, their life is a testament to how things have not worked out for them. Nobody would appeal for your sympathy unless their dignity had been seriously worn out by the weight they've carried in life.
2. It's kinda like a job. Well, it is. If they're putting in their time selling you the Big Issue, calling you "folks" (the guy outside the Somerset House) and doing little poses/stands that might entertain you enough to pause for a mili-second (outside Boots near Charing Cross station), sometimes not, then contracted job or not, they're no different from the guy who hands out the Evening Standard or the pencil-skirted woman who clocks in her hours in Canary Wharf or, basically, you. Sparing them a bit of change and a smile simply becomes an appreciation of common survival in a capitalist society.
Of course, these probably aren't reasons enough for you to give up your laundry change, but theoretically, they seem sound, and won't it be cool if theoretical soundness translated more fluidly into practice.
Image from http://www.jokeoverflow.com/wp-content/uploads/2011/07/not-all-beggars-are-heartless1.jpg