The 5 istarisIstari were sent from Valinor to Middle Earth to monitor and, if found, then crush, any remainder of Melkor's army trying to pursue their master's aim.
To do so, they needed discretion. They don't care about being seen, but they have to not be uncovered. Since elves are, during the Third Age, very less numerous than men, and are immortal. Coming under an elf shape, doing great magic and crushing evil is bound to catch some attention. And
And those elves, who you have no tracks of them before the moment they came to Middle Earth although they overmatch in power the elves who saw the upon the Light of the Two Trees in Valinor (whose a few only are still alive during the Third Age), will look very suspicious to the ennemy.
In my opinion, the point lies there. Elves are very easy to track, since they aren't many of them, a few of those have great powers to notice, and being immortal, those having their own "signature" are living for a long time since in Tolkien's work, the ower comes from the ancientness. So
So, if you want to go underneath, a human is the best choice.