No. The annotation choices referred to in the question that are currently encountered in in some dependency treebanks are not well motivated linguistically.
The question is centrally concerned with the structural analysis of simple sentences like Frank is hungry. Should the subject Frank be construed as a dependent of the copular verb is or of the predicative adjective hungry. These two analyses are illustrated with the next trees:
As the question indicates, the dependency grammar (DG) community is split on this issue. Theoretical DG has for the most part opted for the analysis in the first tree since about the early 1980s, whereas many in the NLP community (natural language processing) now favor the analysis in the second tree. In particular, the Universal Dependencies (UD, https://universaldependencies.org/) annotation scheme opts for the analysis in the second tree. The UD annotation scheme chooses to subordinate function words to content words as a matter of principle.
There are many linguistic considerations that motivate the analysis in the first tree over the one in the second. One of these linguistic considerations is subject-verb agreement. The analysis in the first tree links the subject directly to the finite verb. This is well-motivated because subject determines the agreement morphology of number and person on the finite verb. The second tree, in contrast, does not accommodate this agreement relationship.
Another linguistic fact that supports the first tree over the second is VP-ellipsis. VP-ellipsis elides the complement of an auxiliary verb, e.g.
(1) Fred is hungry, and but Frank isn't (hungry).
Given the analysis in the first tree, the material that remains after ellipsis here (i.e. Frank isn't) is a subtree, whereas it is a not a subtree on the analysis in the second tree. In other words, VP-ellipsis elides a complete subtree on the first analysis, but not on the second.
Yet another linguistic argument in favor of the first tree is case assignment. The nominative/subjective case can occur only in the presence of a finite verb. If no finite verb is present, the accusative/objective case appears instead, e.g.
(2) a. I am hungry.
b. *Me am/is hungry.
(3) a. *I being hungry, ...
b. Me being hungry, ...
This situation is accommodated if there is a direct link between the subject pronoun and the finite verb (if one is present). If there is no such direct link (as is the case in the second tree), one would have no good means of predicting when the nominative/subject form of the pronoun appears. In other words, by linking the subject directly to the finite verb, one accounts in a straightforward way for the case assignment that runs from the finite verb to the subject.
My coauthor and I go into these issues in great detail in our article here: https://www.glossa-journal.org/articles/10.5334/gjgl.537/
In sum, the question points to an issue that continues to motivate much discussion in the DG community about the best structural analyses of many construction types. For me, the issue should never have arisen since the arguments in favor of the one analysis over the other have been clear all along. It would be great if someone from the UD community were to respond on this, providing an alternative answer.