While inheritance laws in Southern Europe are weird, I don't think that partial ownership of buildings is the issue here.
The real issue is that old buildings are not useful anymore:
1. Buildings that are not longer needed. For example, you can walk in woods and see old, run down, metati [1] in Italy. While chestnuts still keep a sentimental value, mountain people do not rely on them for sustenance anymore. Therefore, the drying sheds and mills have been abandoned.
2. Buildings that are not just functional anymore. Our barn had 20 stalls. It was functional as of the 1800s, but it's no longer a viable building to host a herd of milk producing cows. It has small stalls, lack of windows, difficult sanitation. People just build new barns and abandon the old ones. The problem is that the barn is build of rock, so it won't decay so easily.
3. Buildings that are no longer comfortable. Similar to point 2, old stone houses are not that comfortable. Having 3-foot wide stone walls for each internal room seems like charming until you realize that you can't use wall space. A house with a regular footprint (maybe 100 sq. feet) is much smaller once you consider all the space that stone walls take up. Plus, old houses don't have plumbing, electricity, etc, are damp and cold in the winter (but somewhat pleasant in the summer). People just prefer to live in a modern place rather than fix up an old one (which might be marked as historical and will need much more money to fix up).
[1]: https://www.tuscany-exclusive.net/metato/