If you look at your Manage Your Kindle page on Amazon (the same page where you set the email address up) you can see that the Kindle email address is specifically assigned to one Kindle device. If you had more than one Kindle device, then you can assign different email addresses to each. The upside of this for Kindle owners is that you and other family members can both have Kindle's on the same account (and thus share books) but you can avoid bombarding anyone else with your documents (if you did want to send to both at the same time, you just list both addresses in the "To" box when you send the email).
The fact that Amazon don't allow you to set up an email address for any non-Kindle device (and I have the Kindle app installed on my laptop as well as my phone) suggests to me that they're keeping the conversion service as a "value-add" incentive for people who've bought a Kindle device. It's also worth bearing in mind that the conversion process will use some of their computing resources and cost them (albeit a tiny amount compared to the rest of their business) this could be the reason that it's only open to paying customers.