One way of getting around this is to use the center function in an Overpass query. (Documentation here.)
Normally, a query for museums gives us what you picture above: nodes as well as ways, depending on how the object exists in OSM. By appending
center to your
out statement, you'll get the centroid for the object.
Here is an example query:
And the output:
Even though the Linden Museum exists as a way, we get a node which represents its center. Upon converting to another GIS format, this will be included with the rest of the points.
A distinct advantage of this method is that the center function will also collapse relations to their centroids. It's possible that this could result in a centroid which is not located in any of the relation's parts, but does eliminate any potential duplicates.
You can try the query yourself right here.