My opinion is that if there is a single non-ambiguous canonical
parent, then yes. In the case of polynomial rings I think that the
priority is to fix the following kind of non-commutativity in coercion
sage: cm = get_coercion_model()
sage: cm.common_parent(QQ['x,y'], QQ['y,x'])
Multivariate Polynomial Ring in x, y over Rational Field
sage: cm.common_parent(QQ['y,x'], QQ['x,y'])
Multivariate Polynomial Ring in y, x over Rational Field
This concerns also your use case,in what order will you put variables
in the resulting polynomial ring?
PS: one also need to pay attention to monomial ordering
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