I think this is a great idea. I subscribe to r/dogs on reddit and you cannot imagine the amount of people who ask "should I get a dog?". The answer is generally "yes," but I advise them to make friends so they'll have a list of people to call on if they get stuck at work, etc. You're so right, there ARE a lot of people who can't have pets but would love to care for a dog for a weekend or take one out during the week…
I know another woman that actually volunteers at the Humane Society once per month for 8-hours just to be around dogs, because she would love to have one of her own, but cannot given her work schedule as a consultant.