What if Gollum had lived?

[Moonraker]

I suppose if the Valar had the ability to see the doings of Gollum from afar a bit like how Saruman used the Palantir to look deeper into Middle Earth, then they may not have cared to see Gollum in Valinor. I have no knowledge of what dimensions of power the Valar possessed beyond being more powerful than the Maia. Galadriel used her Mirror for this purpose, she may have had more knowledge of Gollum than she would care to admit. Which also brings me to ask why Gandalf didn't ask to use the Mirror more often? Was it just not as reliable as a Palantir? If it was of no use, then why did Galadriel ask Frodo to look into it?