[Legate of Amon Lanc]

Maybe, maybe not. My personal impression (mostly gathered from the Istari essay and the hearing before the Valar when they were being chosen) is that the five of them were chosen in order to approach the mission from different perspectives, yes, in this way to represent the particular Valar - but only in relation to the mission. In other words, for example, if there was only one Wizard sent - for example Saruman - even in his best, he could have helped greatly the Men or Elves or Dwarves in the struggle against Sauron, help to deepen their knowledge, help them to counter the Enemy's inventions, but he would just as well probably neglected the wild animals and nature and such. So if let's say Saruman succeeded, did not fall, but helped the Free Peoples to defeat Sauron, he would have accomplished that, but half of the forests in Middle-Earth would have been gone since he would have used the wood as simple material to build strongholds or weapons to fight Sauron, or even beautiful monuments to the West and let's say he might have left an "unhealthy impression" in the minds of the Free Peoples, so that even after his fall, they would continue in building new beautiful things and expanding, but on the expense of everything living by itself. That's why Radagast was there, so that these things are not forgotten. Also, when we are already talking about Saruman, he could have easily forgotten the meek and those not especially strong or especially wise, he could have favourized some against the others, and that's again why Gandalf was supposed to come along. And so on. In the same way, Radagast alone would have neglected the "civilized people" on the expense of the nature. Gandalf could have neglected some of the really "high stuff" and would not possibly provide the information, power etc. necessary to discover all the Ring-lore in time and even to drive Sauron e.g. from Dol Guldur in the first place.

So this is how I see the necessity of having the five of them. They had a certain purpose - helping, supporting the inhabitants (including the beasts and nature itself) of Middle-Earth to fight against Sauron. That is how it is specifically said. Of course that leads indirectly to many different activities. But that was not "the mission". The fact that Gandalf cheered up many hobbits by randomly performing some fireworks might certainly be even equally important to anything else he had done, but it was not intended. I would compare the activities of the Istari to the Great Music. "Play the Music, and adorn it by whatever special ideas you wish, according to the special individual gifts of each of you." - "Look, go to Middle-Earth and help them fight Sauron, and use all the tools in your disposal, according to the special individual gifts of each of you." The fact that Saruman might have accidentally helped people of Middle-Earth to invent the wheel (to use a silly example), which was subsequently used for many useful things, is a good, but unintended outcome. He was not supposed to go to Middle-Earth and start inventing wheels and steam engines and computers, he could have spent years with that even if it was his only purpose. But if his intention to help the people led him to do this - "yeah, we'd protect Minas Tirith much better if we use this new project of mine to rebuild the walls in 45° angle" - then why not.

As for the last paragraph you mentioned, I think we cannot say much about Alatar and Pallando. Tolkien himself implied that he fears they failed, in a similar way to Saruman. But we don't have really sufficient information to say one or the other.