Restoring historic gardens seems to be quite a craze at the moment so it's not surprising they want to restore the summerhouse as well. Monmouth is the home of the Nelson Museum and His Lordship made a historic visit to the town so maybe there's also the hope of luring the tourists by exploiting the link, however tenuous, with a great love story.
It's certainly worked in Verona, the home of those two other famous lovers, Romeo and Juliet, where the house 'said to be' the home of Juliet Capelli, the 'inspiration' for Juliet of Shakespeare's famous play, is now a 'must' on the tourist trail. There's a statue of Juliet, and a wall where you could leave messages about your beloved - though I think they've just had a cull of these - all based on a legend.
All the world (except Tony) loves a lover!

Another link with Nelson in Monmouth was the Beaufort Arms, the hotel where Nelson and his party were accommodated. It was recently converted into flats and the Nelson Suite was for sale. I was tempted to 'downsize' but the lack of a garden dissuaded me.