Indeed, nothing in the rules prohibit it. However, nothing in the rules indicates that it is what is meant to be done either, and in an exceptions-based rule system (which D&D is), explicit instructions are required to constitute a rule.
That really isn’t what’s going on. One rules interpretation is well-supported with specific citations from the rules. The other relies on assuming some of the text in the rule book is not rules text, and/or inferring some specific exceptions to the general rules that are not (as far as has been demonstrated in this thread) explicitly present in the text. That doesn’t mean the latter interpretation is house rules. It just means it is less epistemologically sound than the former.