The Force Awakens (SPOILERS)

[Sephiroth]

This is why I will always argue that Anakin really was the chosen one. Balance is equal. There were plenty of Jedi running around doing all kinds of things in the Galaxy, and only a handful of Sith. After Anakin's betrayal there were only two Sith (him and palpatine), barring any hidden Sith hanging out wherever in the galaxy uncanonically, and two Jedi (Ben and Yoda), barring any hidden Jedi hanging out wherever in the galaxy uncanonically.

But plenty of Jedi are totally irrelevant when the master of the Sith has manipulated the force so much that he alone is able to use it to perfection (or pretty much) and is superior to the Jedi.

It's dumb, but the Jedi interpreted the prophecy and "balance" as ridding of the Sith entirely. I still have no clue why they would think that, but I guess when you are in control for thousands of years even Jedi gets a bit of an ego.

Plagueis/Sidious were responsible for the imbalance of the force. With them gone the power that manipulated them would be gone as well. Sith being gone is not the same as the Dark Side of the Force being gone, just the cause of the imbalance being gone - and probably also the balance restored.

You may also not misinterpret Dark Side Users as Sith. Sith are not all Dark Side Users and Padawan and Jedi are not all Light Side Users. Those are ideologies and not the terms for everyone using the force. Kylo Ren is also not a Sith (except if Snoke is one). I know in general those terms are used, I also used to do that but my brother who is more familiar with Star Wars told me.