I think were looking at this as too much of a one dimensional process. You can memorize and understand at the same time. I know a brother who listened to the tafseer of Surah Hujurat, and as he listened to it, he started memorizing it. Understanding and memorizing go hand in hand. They should not be separated.

However, before we even mentioning that, I think its important for us to realize something about the Quran, that the Quran is not a book of information but rather a book of transformation. It was designed for us to read, contemplate, and act upon. Although reciting the Quran without knowing it does in fact impact the heart of the believer, wallahi, nothing compares to actually understanding it. Every scholar can attest to that fact. Even the English translation doesn’t do justice to the nuances that exist from the Arabic language. As Imam Suhaib said, its like playing Atari versus PS3.

We should remember that understanding is the most important thing. Not to say that we should forsake memorizing, especially when you are young. We should encourage the youngins to memorize the Quran. But we should always keep in mind that the Quran was meant to transform people. It is a transformative text.

Your comment makes sense in light of the fact that as a person grows older, his brain shifts focus from memorization to analysis. An old saying goes, “Memorizing something in youth is like engraving on stone; memorizing something in old age is like engraving on water.”
I think we can all agree that practicing the Qur’an in our 24/7 daily lives takes precedence over memorizing it. But maybe memorizing it first and then understanding and contemplating on the meaning can help us practice it?

Therefore, I personally encourage people to regularly recite Quran first, whether they understand it. Most Muslim now days do not even read a single page of Quran a day. And some of them, when advised to read comes up with the excuse that reading would not make much difference since they do not understand the language of Quran. To them, I say, “Recite the Quran first, listen to it, and do them regularly, if you truly want to break this vicious cycle.”