How to save entire term lineage
Depends on your understanding of reasonable. Until hierarchical select or similar modules become available you could save the parent terms programmatically on node save - the code probably wouldn't exceed 30 lines or so, especially when you don't have many taxonomy fields where you want to do this. 

You can access a term's parents with the following code utilizing TermStorage:

$parents = \Drupal::entityTypeManager()-&gt;getStorage('taxonomy_term')-&gt;loadParents($termId);


Then you only need to go recursively through the tree and grab all parents (if your terms can have more than one), get their ids and set them in the node you want to save.