Many questions can be asked about the Istari, or the Wizards as we like to call them in our own tongue, and many answers can be given. Some might be closer to truth than others but that they were send to Middle-Earth as emissaries from Valinor to aid the people in the wars against evil can not be doubted but why it was those five it ended up with and who chose them is quite interesting and some answers can be given while new arises.
The fullest account of the Istari was written in 1954 and is published in Unfinished Tales but it is not the latest. The latest text involving the history of the Istari begins in a text concerned Glorfindel, written in 1968 and published in the book Peoples of Middle-earth. From that text arose some considerations in the mind of J.R.R.Tolkien and made him write some new things about the two blue wizards, Alatar and Pallando. Those thoughts were never incorporated into the Annals but does that make them less valid ? I do not know and will let you consider it yourself. The only thing I can say about them are they were the latest writing concerned the Order of the Istari. In between these two accounts J.R.R.T wrote in a letter [ Letters, 211 ] an answer regarding the two Blue Wizards.
Text in [ ] is mine for further explanations. Text in ( ) is C.Tolkien. Text in Italic is quotes from the actual texts.
The earliest account; UT. 1954 :
Manwë summoned the Valar for a council [ Maybe he had asked Eru for counsel ] at which it was resolved to send out three emissaries to Middle-Earth and he asked who would go. They would have to loose might and clothe themselves in flesh to win the trust of Elves and Men but this would also imperil them, diminish there wisdom and knowledge and bring upon them fear, the care and weariness of the flesh. Only two came forward; Curumo [ Saruman ] and Alatar. Curumo was chosen by Aulë among "his" Maiar and Alatar was send by Oromë. Manwë asked where Olórin [ Gandalf ] was and Olórin just returned from a journey and coming to the meeting asked what he wanted from him and Manwë told that he wished him to go as the third to Middle-Earth. Olórin answered that he meant himself to weak for such a task and that he feared Sauron. Then Manwë said that that was all the more reason why he should go and he commanded him to go as the third. There Varda broke in and said "Not as the third". and Curumo remembered that.
The tale ends with the statement that Curumo was obliged to take Aiwendil [ Radagast ] with him to please Yavanna, Aulë`s wife and that Alatar took Pallando as a friend.
The relations between the Istari to the Valar are : Curumo to Aulë, Olórin to Manwë and Varda, Aiwendil to Yavanna and Alatar + Pallando to Oromë. This might also explain why Alatar and Pallando the Blue Wizards passed into the East. In the youth of Middle-Earth Oromë often traveled and hunted in those regions and therefore "His" people might have had a better knowledge of those lands. It might also explain why Saruman did not like Radagast; he was imposed to him and not taken by free will and also explain his rather unfriendly feelings towards Gandalf because he heard Varda´s words and saw the mightiest Valar choose Gandalf. in fact ordered him to go because he was badly needed.
Letters, 211; 1958.:
I really do not know anything clearly about the other two [ the Blue Wizards ] I think they went as emissaries to distant regions, East and South, far out of Númenorian range. What success they had I do not know ; but I fear that they failed, as Saruman did, though doubtless in different ways; and I suspect they were founders of or beginners of secret cults and "magic" traditions that outlasted the fall of Sauron.
In this letter something about the names of the Valar and Maia ( which is interesting as the Istari was of the Maia ) is told. These archaic beings " had no language of their own as they did not need one and thus they had no need for true names, only identities, and their names were conferred on them by the Elves were in origin nicknames, referring to some striking peculiarity, deed or function ( The same is true of the Istari or wizards who were emissaries of the Valar and of their kind.)"
The second account; Pme. 1968. :
Concerned the blue wizards Alatar and Pallando :
In 1968 Tolkien wrote a text of five pages [ the last of this issue ] with some thoughts of the matter of Glorfindel. In these he says that "it seems far more likely that he was sent in the crisis of the Second age when Sauron invaded Eriador [ War between Elves and Sauron ] to assist Elrond and that though not ( yet ) mentioned in the annals recording Saurons defeat he [ Glorfindel ] played a notable and heroic part" In the end of this note he [ Tolkien ] wrote the words " Númenorian ship" presumably indicating how Glorfindel might have crossed the Great Sea [ Authors note, C.Tolkien ]
C.Tolkien notes that "we may best suppose that Glorfindel returned during Second age before the shadow fell on Númenor and while the Númenorians were still welcomed by the eldar of Eriador as allies. It must then have been as early as S.A.1200 but could be as late as S.A.1600."
Another note by J.R.R.T, written same year or later because it arose from his considerations of the above mentioned text about Glorfindel, named "Note on the landing of the Wizards and their functions and operations" In this text [ Not published in the UT but mentioned by C.T as nearly unreadable ] J.R.R.T says that the three wizards Saruman, Gandalf and Radagast came at the same time but Saruman came alone whereas Gandalf and Radagast came together and then :"The other two , [ the Blue Wizards ] came much earlier, at the same time probably as Glorfindel when matters became very dangerous in the Second age".
Same note and exact quoting with missing words " But the other two Istari were sent for a different purpose. Morinethar and Rómestámo ( Darkness-slayer and East-helper ) Their task was to circumvent Sauron : to bring help to the few tribes of Men that had rebelled from Melkor-worship, to stir up rebellion... and after his first fall to search out his hiding ( in which they failed ) and to cause ( ? dissension and disarray ) among the dark East… They must have had very great influence on the history of the Second age and Third age in weakening and disarraying the forces of East… who would both in the Second age and Third age otherwise have… outnumbered the West."
This is the latest of J.R.R.T`s thoughts of the Blue Wizards, when they came, what they came for and of their rate of success. I think it is remarkable to find new names of those two and also to read his final thoughts of them even it was never incorporated into the annals. It seems J.R.R.T did not think they failed their task utterly even he feared they maybe failed. A magic or secret cult is not necessarily meaning also worshipping Melkor or Sauron even it is a Fall.