I think it would be neat addition for monuments to provide some sort of morale, loyalty or control boost in the regions they're erected.
No, it was decided when the feature request was created in 2012 to keep them simple.
On that note, more infrastructure for regions in general could be fun!
This is already an approved TODO, in terms of estate holders (knights) being able to build local buildings. For probably as long or longer than 2012. Alas, limited volunteer developers means no one has worked on it. It is a larger undertaking.