There are a number of ways to get Prime for essentially-free or even straight-up free. Students can get it free for a year [1], and Amazon Mom [2] provides it essentially free for parents of young children. You have to buy $25/month of qualifying goods, but we have not found this to be a challenge if you're still on diapers. (And Amazon is quite competitive on diapers.) YMMV.
It seems to me that Amazon is desperate for you to have Prime, but as what is basically a loyalty program, it doesn't work for them if they simply give it away. The customer has to feel engaged somehow, either by paying for it, or feeling like they're getting something really valuable for some promotional reason. I personally suspect that as the Amazon Mom's year ends or the student's year comes up that the announcement will be made that out of the goodness of their heart, Amazon has decided to simply extend the program for another year or something, and that as they can work out reasonable excuses to give you a free Prime subscription they will continue to do so. Just my best guess based on the business situation.