[RPG] Does the Keen Mind feat allow a Wizard to have prepared all his spells

The question is different from this one.

Disclaimer: I want to clarify something. My question is not meant to find a way of breaking the class or whatnot. My question is because I am curious of if it is possible.

I see that it is possible for Keen Mind to bypass the Wizard limitation on number of spell prepared per day. The reason would be (PHB 114):

Preparing a new list of wizard spells requires time spent studying your spellbook and memorizing the incantations and gestures you must make to cast the spell: at least 1 minute per spell level for each spell on your list.

Emphasis mine. From the mechanical point of view, the Keen Mind feat allows you to completely memorize something that you have seen. Since you have to study and memorize your spells, that would mean that the Keen Mind feat might be used to memorize all your spells.

Keen Mind:

You have a mind that can track time, direction, and detail with
uncanny precision. You gain the following benefits.

• Increase your Intelligence score by 1, to a maximum of 20.
• You always know which way is north.
• You always know the number of hours left before the next sunrise or sunset.
• You can accurately recall anything you have seen or heard within the past month.

Emphasis mine. Since studying and memorizing is, well, much more focused than just seen and hearing, there is not limitation on that side. Also, from the perspective of that a specific rule overrides a general rule (PHB, page 7), the specific rule of the feat might invalidate the general rule of the wizard.

Remember this: If a specific rule contradicts a general rule, the specific rule wins.

That is from the mechanical stand point. But from the RP point the wizard memorize his spells easily from "years" of practice, reading and a high intelligence to boost. Little has to do with magic or a magical mind. Just plain and crude practice.

You prepare the list of wizard spells that are available for you to cast. To do so, choose a number of wizard spells from your spellbook equal to your Intelligence modifier + your wizard level (PHB, 114)

The feat would imply that the wizard has an unusual sharp mind to remember and recall details quickly over a specific time. Once that time is passed, if there is not feedback the memory become foggy and unreliable (the spell just might kaboom in his face).

So, it seems that is possible, but, is it really possible (regardless of how OP that might be)?