It does not have to be Photobucket ... here is about 30 options:
http://en.wikipedia.org/wiki/List_of_photo-sharing_websites
The point is TFP does not have the resources to store the 10,000s of images. That requires storage space and computer support, etc. All of that requires $$$. If you have not noticed, there are ZERO adds on this forum, how many other forums are like that? There is $0 required to be a member and ask all the questions you want. If a MUCH larger % of our members actually donated to become supporters, well, then maybe there would be $ available to upgrade the hardware and host people's photos.
See that big button at the upper left of the page that says
Become a TFP Supporter!! Click it. There you can see one way of upping your storage space from 256kB to 10MB.
If you do not want to do that, well, host them somewhere else that does not require the viewer to sign up. If you do it right, there is no need for the reader to click on anything to see your photos. Personally, I rarely click on a link to an album.