It has probably occurred to you at once that if they could afford to put up this fairly impressive chunk of masonry they couldn't have been all that hard up, and indeed, the story preserved in popular memory is that the Duke took the same view and promptly put their rents back up again. I seem to remember reading somewhere that this story is historically unfounded. The most likely interpretation would seem to be that the tenant farmers saw it as a shrewd investment, a calculated piece of schmoozing that would make it hard for the Duke to become more demanding in the future.
Alas, it is no longer possible for children to climb all over the lions, because railings have been erected around the base to keep out the vulgar masses. This was part of the original design, but the original railings were taken away during World War 2 as part of the drive to recycle every possible piece of scrap metal into armaments. Because my grandfather was on the town council at that time, I have inherited a copy of the newspaper report of the council's debate on whether or not to agree to part with this piece of their 'built environment'. Some members were extremely unhappy about sacrificing their elegant railings, but my grandfather argued strongly that this was a very trivial sacrifice compared to what they were asking of their young men at the front, and his side carried the day.
And for sixty years or so the children of Alnwick played happily around the railing-free plinth. It was only a few years ago that new railings were put up, in line with the currently prevailing orthodoxy to Restore and Conserve everything in sight back to its Original and Authentic condition. Why can nobody ever admit that the original form of something is not always the best?