NO SHIT SHERLOCK! Ofcourse this is the reason Sony does this. Its called marketing.
But if they diddnt gave you, you where also whining..
If they give you 10$ it will cost them to much money (70 million x 10$) thats impossible.. Showing they care about customers they give u 30 days free, where u normally have to pay for. And they dont commit you to subscripe again, but obv its something they hope u will because u have an free smell on PS+ now..
PS+ only earns them money