Did the Valar make a huge mistake?

[obloquy]

the fact remains that one who has pure intentions like Manwë is not infallible, only Ilúvatar is

You're still missing the full scope of the information provided from Osanwe-Kenta.

One more time I'll point to a portion of the quote:

...Manwe was wiser; or being ever open to Eru he did His will, which is more than wisdom....Manwe was bound by the commands and injunctions of Eru, and would do this or abstain from that in accordance with them, always...

Any decision of Manwë's was in accord with Eru's will, which does make Manwë infallible. That's not to say that Manwë couldn't rebel, but he never did.