First of all, the verse in the Surah Waqiah is not related to ablution (wudu) at all. Let us read these verses together with the previous ones:
فَلَا أُقْسِمُ بِمَوَاقِعِ النُّجُومِ وَإِنَّهُ لَقَسَمٌ لَوْ تَعْلَمُونَ عَظِيمٌ
“Then I swear by the location of the stars. And if you could know, it is a great oath indeed.” (56:75-76)
The importance of the location of stars is explained in the 37th chapter:
“Indeed, We have adorned the nearest heaven with an adornment of stars. And we protected it against every rebellious devil. [So] they may not listen to the exalted assembly [of angels] and are stoned from every side. Repelled; and for them is a constant punishment.” (37:6-9)
The nearest heaven is the first heaven.
Going back to chapter 56, and reading together with the first two verses:
إِنَّهُ لَقُرْآَنٌ كَرِيمٌ فِي كِتَابٍ مَكْنُونٍ لَا يَمَسُّهُ إِلَّا الْمُطَهَّرُونَ تَنْزِيلٌ مِنْ رَبِّ الْعَالَمِينَ
“Then I swear by the location of the stars. And if you could know, it is a great oath indeed. It is a prosperous Quran, in a ‘maknun’ book. None touches it except the purified. Sent down by your Master.” (56:75-79)
The word ‘maknun’ stems from the root ‘scabbard’. You cannot touch a sword when it is inside its scabbard. This word is explained in the very same chapter, verse 23. It mentions while talking about huris: “They are like ‘maknun’ pearls”. (56:23)
There is no way to touch the pearls that are hidden in oysters. The Qur’an that cannot be touched is like that pearl in the oyster. It is apparent that the books of Quran, that we currently touch and recite, are not subject to such a protection, since we are already able to hold them in our hands.
The Qur’an that is in the location of the stars is protected against the devils. Devils are repelled from the first heaven, according to 37:9, so that they cannot enter there. Devils that attempt to enter the first heaven are not purified. Since human beings are also not able to reach there, the only purified beings that are the subject of this verse are angels.
Then, the Qur’an that is the subject of these verses is the one in “lawh mahfooz”, which is placed and protected in the first heaven, and can be touched by angels only.
Another important point: “لَا يَمَسُّهُ إِلَّا الْمُطَهَّرُونَ = None touches it except the purified.” is not an imperative sentence in Arabic. That means, it does not decree a command, but rather it affirms the current state. Nobody, except the purified, which are angels, do touch it.
Since it IS possible for people without ablution to touch the books of Qur’an currently, this sentence cannot be about the Qur’an we have in hand, on earth.
Then, the verse 80 goes on: “Sent down by your Lord” because, Quran was in Lawh Mahfooz and was sent down, so that we can touch and read. Otherwise nobody could take it from there.
Ablution is pre-requisite of prayer (salat) only. In the verse:
“O believers, when you raise for prayer, take ablution.” (5:6)
About the case of needing major ablution (ghusl) for prayer, it is commanded:
“And if you are in a state of janabah, purify yourselves.” (5:6)
The only ruling about reciting Qur’an is in the verse below:
“When you recite Qur’an, seek refuge in Allah from the stoned devil.” (16:98)
That is, saying “A’uzu billahi min ash shaitani r rajim ” before beginning to recite Qur’an.
Another significant mistake is about women. Although it is not true: Suppose that men are junub; they can have major ablution and recite the Qur’an according to tradition. However, traditions prohibit women from reciting and touching Qur’an in case of menstruation, too. This is such a long period and distance that is wrongly (or deliberately) set between women and Qur’an. There is no evidence, not even a weak hadith about this.
It is also interesting that nobody objects if non-Muslims read or touch Qur’an. However, when Muslims intend to touch it, they are questioned about ablution.
Also asked: “Wouldn’t it be better if people took ablution?”
No, it is not better at all. Because you may need to touch Qur’an to check something quickly; and when you go for ablution before that, something else would most probably interfere with you. Thus, ablution would be an obstacle between you and Qur’an.
Consequently, lack of ablution or major ablution, and menstruation of women hinder prayer only, and nothing else about Qur’an.