I believe that the old moniker "If you don't value your time why should anyone else" rings true here. Giving it away for free may indeed give you great experience *if* you can allow people to let you into the fold. Consider startups that *can* take on interns but don't simply because its a chore to see a good example of this in motion. If you're not creating value in yourself you're certainly not going to translate that value to your clients, customers etc..
In my 20 years as a labor economist and business consultant, the one thing that is most crucial in these major decisions is (pardon the pun) "clarity."
Perhaps you could give me more detaisl on what services you would be offering for free, and why you feel you need to offer them for free? What EXACTLY would be your ultimate best outcome where your specific purpose, passions, and perfect skills would all align? Not to be trite, but my experience has shown that, "exact outcome goals make for exact outcomes."
The more details you share regarding what you REALLY want to do, the more the road to get there (specific opportunities, ideas, people that can help, the costs, the rewards, etc.) will illuminate and become clear.
Also, unless you are called to a life of charitable full-time purpose - which is very nobel, personally I am not a fan of offering "free" services that have value of any kind. Experience has shown that the recipient of "free" services rarely converts to paid opportunity because they don't have much investment/"skin in the game" to care enough if you succeed. An example of this in the early days of my own business are when I offered 2 month "trials" of our annual services (annuals that we're normally priced around $50,000 - $500,000/yr.) to larger companies as a way to "get in the door." What I learned after 3 years was that the "free" trials converted to annual customers at a measly rate of 6%!
However, even offering those same types of customers the same trial but with a heavily discounted price of even as little as $2,000 for 2 months to try us, the conversion rate when to 82% with an average annual contract of $104,000! After that, those annual contracts would renew each year at around 98%!
Hope this helps. Feel free to call me if you have any follow up questions.