Further to this, In my test app, I loaded the v2.16 EsriLoader, without using any react classes or components, and the ExaggeratedElevationLayer is still working there. So this is not necessarily an issue with the older esriLoader version, or the older JS API version.
Sample app is here: https://codepen.io/tthompsonEsri/pen/XWayRqw?editors=0010
Seems specific to react classes, still trying to narrow it down.
Update:
Built out a custom component and passed it to the react Renderer(). It basically completely overlaps the React-arcgis.Scene component and does display the ExaggeratedElevation without issues. It's a lot of extra coding, but seems to work around the issue.
https://codepen.io/tthompsonEsri/pen/VwzqNaX
Another Update:
Slightly more refined solution where the Scene in the child component is not overwriting the parent scene component.
https://codepen.io/tthompsonEsri/pen/mdMoWwL?editors=0010