Mesh Simplification Algorithms
According to Polygon-Mesh-Processing, section 7.2.2. paragraph "Error quadrics"


  Error quadrics have major advantages regarding memory consumption and computational efficiency: each vertex $x$ stores a symmetric 4x4 matrix $Q$ only, and the error can efficiently be computed in constant time as $x^T Q x$ - no matter how many planes are associated to vertex $x$ during decimation. Because of this, error quadrics are one of the most frequently employed techniques in mesh decimation.


The author of the reference I mentioned specifically refers to the paper you mention in your question. My interpretation is that more recent methods might be more sophisticated but resource-wise quadric errors are still better.

Also I'd add is relatively easy to implement anyway.