There is no ruling that a Muslim MUST read Qur'an. It's extremely recommended. Better to memorize its verses.More than that, it's recommended to the reflect in Qur'an. Even more than that it's important to apply Qur'an in our lives, use it as a touchstone.
Many of us have Qur'an at our houses as a decoration, many of us memorization of Qur'an without any reflection and many of us have reflection without any application. It's just that we can/should always get better and better. So a person that has memorized Qur'an has done very well, but 2 more major steps left to go for.
وَقَالَ الرَّسُولُ يَا رَبِّ إِنَّ قَوْمِي اتَّخَذُوا هَٰذَا الْقُرْآنَ مَهْجُورًا
And the Messenger has said, "O my Lord, indeed my people have taken this Qur'an as [a thing] abandoned."Furqan :
carrying Qur'an like a donkey is about one who just reads Qur'an but doesn't apply:
مَثَلُ الَّذِينَ حُمِّلُوا التَّوْرَاةَ ثُمَّ لَمْ يَحْمِلُوهَا كَمَثَلِ الْحِمَارِ يَحْمِلُ أَسْفَارًا ۚ بِئْسَ مَثَلُ الْقَوْمِ
الَّذِينَ كَذَّبُوا بِآيَاتِ اللَّهِ ۚ وَاللَّهُ لَا يَهْدِي الْقَوْمَ
The example of those who were entrusted with the Torah and then did not take it on is like that of a donkey who carries volumes [of
books]. Wretched is the example of the people who deny the signs of
Allah . And Allah does not guide the wrongdoing people.Al-Jum'ah :
أَفَلَا يَتَدَبَّرُونَ الْقُرْآنَ ۚ
Then do they not reflect upon the Qur'an Nisa' : 82
وَإِذَا قُرِئَ الْقُرْآنُ فَاسْتَمِعُوا لَهُ وَأَنصِتُوا لَعَلَّكُمْ تُرْحَمُونَ
So when the Qur'an is recited, then listen to it and pay attention that you may receive mercy. A'raf 204
In addition from a psychological perspective the more you bond physically with something the better it gets. I mean if you read Qur'an in your head, or read it out loud, or also read it with the book in your hand, it will all be different.
Having that said the most important element of doing (reading/ listening / performing anything) is the presence of your conscience. Let me explain what I mean.
I'll go from bad to good:
Have you done your daily prayers but then you were thinking about how to solve a math problem and never realized how you began or finished your prayer? Or just read your prayers quickly just because you had to.
You've read your prayers but during some rak'ats you were thinking about what your colleague told you?
You've read your prayers but you were really just reading/saying it. You didn't truly mean what you said. Like reading 200 pages of a book but then if someone asks you what was it about you'd be like : "ummm...uhhh...it was about a guy fighting evil (not remembering any of the details"
You've read your prayers but this time you were paying attention to the words, when you said ایاک نعبد و ایاک نستعین you really really meant it. In your heart you were like " FIRMLY, my compassionate lord, I will only seek from you and not seek from others, you sustain me". When you say صراط الذین انعمت علیهم غیر المغضوب علیهم و لاالضالین you really try to purify yourself from the wrong path, you only want to be on the path of the prophet.
You've read your prayers and in addition to the above, you see heaven on your right and hell on your left, you see death imminent, you're fearful of your sins,etc.
Basically the most important thing is how deeply you translate (to your current moment) what you're reading/hearing
(The steps for reading Qur'an are very similar, but I feel this example better connects with our daily prayers. In Qur'an whether you just read it, or when you read verses of Akhlaq you look into yourself and say " What have I done?! I've deceived myself"...when you read verses about heaven and hell "you see death imminent and tell yourself this world is only to be traded for the value of paradies, when you see verses of Allah being just, you look into yourself and tell yourself it is me who's brought this misery upon myself, when you see verses that Allah aids his believers you become calm and patient, etc. )
And based on my experience when you're reading from Qur'an you're bringing your eyes' focus to the Qu'ran. If you're reading from memory then you could also be seeing someone moving in front of you, the reflection of light, notifications from your cellphone, etc.