Yes, and no, Minister.
Hierarchy will not die off because it is a core part of the way that the mind organizes concepts- for example, prototype effects imply several different levels.
Folk Taxonomies are hierarchical, though the depth is usually smaller than that of scientific taxonomies and the principles of organization is usually different.
There can be many ways of arranging the same concepts, and although it is possible to show that some are incorrect, it is in general impossible to show that one and only one Ontology is correct; this follows from the indeterminacy of translation (Google Gavagai!)
Attempts to force an alien Ontology onto subject matter experts breaks them. They just stop performing at an expert level.
It is usually possible to develop a suite of ontologies that are logically interoperable, but this requires experts who have skills from a variety of disciplines AND who are capable of deferring to the SMEs on how they see the world. It may be necessary to have intermediate mapping ontologies, but if the ontologists working with the different communities of interest are careful, these mappings can avoid losing meaning.
Tagging as ad-hoc keywords does not work for data interoperability; it also usually fails to achieve good recall. Flat lists of controlled terms are usually difficult to apply unless they are very small. When Thomas Vander Wal coined the term Folksonomy, it was intended to cover the same kinds of structures as folk taxonomies. Its subsequent application to describe unstructured lists of tags was a misappropriation.
RDF and OWL added some extra problems. They were designed without much input from people with actual use cases, and optimised for the wrong things. Some things were dumbed down because some people didn't understand what had gone before, and could not understand why the old folk were kicking up such a fuss. Other things were constrained in order to make OWL DL decidable, even though the resulting worst case complexity of 2-NEXPTIME means that implementations have to work on special cases, check for too slow results, and / or limit expressivity to sub profiles just in order to work.
Other design decisions did not consider the human factors of using OWL. It is very difficult to explain to people why restricting the range of a property for a specific class is handled by adding an unnamed superclass. It is also difficult to explain the Open World Assumption, and the non unique name assumption. It is also hard to explain why, in a web environment with no standard world closing mechanism, making everything monotonic is necessary.
It is especially hard to justify the restriction of RDF to binary predicates- some predicates are intrinsically of higher arity; just because higher arity predicates can be misused, and it is possible to reduce everything to binary does not make it desirable.
Having a model that does not match the existing experience of UML modelers, database designers, or users of other KR systems causes real problems for real users.
Nevertheless there is baby in the bathwater, and it can become soup. It just might not look the same.
The schema.org efforts are limited to the extent that they are barely semantic (a conscious decision by danbri and guha); unfortunately some of the discussions by others show a visceral distain for any questions as to what vocabulary choices would actually mean that is almost anti-semantism.