Your reasoning hinges on the notion that parents are necessarily household members. On a purely formal level, it's not the case, it's an additional material requirement thus explicitely ruling out family reunification with parents qua parents.
That way, I think, the majority of the parents would anyway qualify for residence even if they are in no possible way dependent. They could simply apply through the "extended" family option by stating that they are bona fide members of the household (in the majority of the countries, except Bhutan and some others, parents live together with their Son and daughter-in-law). So almost every son (adult child) can sponsor his parents as they will most likely be bona fide members of the household.
This directly means that ALL parents, regardless of any dependence are eligible to join their adult child in another EU country, as parents in the most cases live with their son. If the EU citizen is a daughter, things are different though.
I don't share this analysis but this doesn't really impact the legal question: your parents need to establish that you formed a household before moving to the EU, not merely that they are your parents. That's in marked contrast to the spouse, minor children and minor children of the spouse, who do not have to meet this requirement.
Furthermore, the language of the directive is actually quite guarded. Let's look at the detail of article 3:
This Directive shall apply to all Union citizens who move to or reside in a Member State other than that of which they are a national, and to their family members as defined in point 2 of Article 2 who accompany or join them.
Without prejudice to any right to free movement and residence the persons concerned may have in their own right, the host Member State shall, in accordance with its national legislation, facilitate entry and residence for the following persons:
(a) any other family members, irrespective of their nationality, not falling under the definition in point 2 of Article 2 who, in the country from which they have come, are dependants or members of the household of the Union citizen having the primary right of residence, or where serious health grounds strictly require the personal care of the family member by the Union citizen;
(b) the partner with whom the Union citizen has a durable relationship, duly attested.
The host Member State shall undertake an extensive examination of the personal circumstances and shall justify any denial of entry or residence to these people.
Here again, there is a direct contrast between the immediate family mentioned in article 3(1), to whom the directive applies, and other beneficiaries listed in article 3(2), to whom it does not. For the latter, member states should merely “facilitate” entry and residence “in accordance with its national legislation”. In other words: They are not entitled to anything under EU law, which explicitely gives a lot of leeway to national law.
The only specific obligation described is “justify[ing] any denial of entry or residence to these people”, which means that such a denial is perfectly allowed and not even limited to specific grounds (as is the case for EU citizens and their immediate family).
The same is true of the recitals detailing the motivation behind the directive:
(6) In order to maintain the unity of the family in a broader sense and without prejudice to the prohibition of discrimination on grounds of nationality, the situation of those persons who are not included in the definition of family members under this Directive, and who therefore do not enjoy an automatic right of entry and residence in the host Member State, should be examined by the host Member State on the basis of its own national legislation, in order to decide whether entry and residence could be granted to such persons, taking into consideration their relationship with the Union citizen or any other circumstances, such as their financial or physical dependence on the Union citizen.
While it does mention extended family members, far from extending the same rights to them, it explicitely states that they “do not enjoy an automatic right of entry and residence”, again citing “national legislation”.
Finally, as detailed on the EU movement website, there is another stipulation, namely that the family must have formed a household “in the country from which they have come”. This is actually a restriction: it means the household must have existed immediately prior to moving to the EU member states. For example, if you studied abroad and started a career there before moving to the EU, you cannot sponsor your parents, even if you lived with them earlier in your life (unless they are dependent on you, e.g. financially). Similarly, if you lived several years in the EU before naturalizing and moving to another EU country, it would also seem to rule out this route as you did not form a household anymore at the time the directive is engaged.