These people that request to have prophecy are called the sons of the prophets. Even though they concentrate their minds, it is possible that G-D's essence will rest on them and it is possible that it will not.
This idea was touched upon by me while discussing halacha 1. I said over there (Yisodei Hatorah 7:1),
Also, the Rambam indirectly tells us that G-D must choose to give a person prophecy even if they do everything that is stated here. It is not a given that a person who even reaches this high level of wisdom and knowledge will also attain prophecy, it is up to G-D to choose who will receive prophecy. However, only someone on this level is even an option for G-D to choose from.Here we can see a similar idea that is more direct than what is stated in the first halacha. The Rambam is telling us that even if someone has reached the level of being a "Son of the Prophets" he or she still might never be granted prophecy.
This idea is discussed at length in "The Guide for The Perplexed" 2:32 (translation from sacred-texts.com),
For we believe that, even if one has the capacity for prophecy, and has duly prepared himself, it may yet happen that he does not actually prophesy. It is in that case the will of God [that withholds from him the use of the faculty]...That those who have prepared themselves may still be prevented from being prophets, may be inferred from the history of Baruch, the son of Nerijah; for he followed Jeremiah, who prepared and instructed him; and yet he hoped in vain for prophecy; comp., "I am weary with my sighing, and rest have I not found." He was then told through Jeremiah, "Thus saith the Lord, Thus shalt thou say to him, Thou seekest for thee great things, do not seek" (Jer. xlv. 5).
Personally, I think that the Rambam mentions this idea here for one main reason, it is a practical way to explain why people no longer have prophecy. Even if someone were to reach a state where he or she could be considered "Son of the Prophets" they don't necessarily receive prophecy according to the Rambam. Had the Rambam said that a person receives prophecy once they reach a certain level of knowledge and concentration then he could be called a liar or even doubt himself. This short sentence takes the ability to attain prophecy out of the hands of man and puts it solely in the hands of G-D in the Rambam's philosophy. This is not to say that Rambam made this up to deflect criticism, only that it was philosophically necessary. Really, the Rambam would have liked to leave it out, but he saw that practically some people attain the level of "Son of the Prophets," but never become prophets.