Tolkien, in a 1954 letter spoke about the Istari and about Gandalf's sacrifice on the bridge and his being sent back, enhanced. Tolkien said that they (incl Galdalf)
"had been sent by a mere prudent plan of the Valar; but the Authority {ie. Eru, the One} had taken up this plan and enlarged it, at the moment of its failure."
That is an interesting comment in that it shows Tolkien considered that the Istari (as sent by the Valar) **DID** fail. Gandalf was the last remaining solid and energetic to the Valar's intents (Radagast having "become enamoured of the many beasts and birds in M.E.", Unfinished Tales) and he had just been killed.
At this point The One stepped in and said, in effect, "You Valar had a good idea, but even *you* need to rely on ME to provide for the succor of M.E." So, as He had (long before) taken up Aule's attempts to make peoples to enjoy Middle Earth, and given being to the Dwarves -- so he now took up the Valar's attempts to encourage and tutor the peoples of Middle Earth in their maturing and growth learned in the struggle against Sauron, and gave new power and profundity to the effort by sending Olorin back, enhanced, to "finish the task".