Having the Internet controlled primarily by the US and US-friendly organizations may not be ideal, but it would be better than having it controlled by a China, Russia, Mid-east dominated body.
The objective of whom? Please, name names. Or don't bother.
If I don't trust the motives and agendas of some of the regimes behind that push, so sue me? The US isn't exactly a paragon these days, and our political system somewhat corrupted by the influence of highly-concentrated wealth, but I also see signs of a long-overdue self-corrective reaction to that, enabled in large part by the open Internet.
Is such a reaction possible in other more restrictive, more authoritarian regimes? Doesn't look like it, and ones like China are doing all they can make sure it stays that way, but who knows. We shall see...
In other situations Russia and China fight to reduce the power of the UN. Mostly situations where western powers are seeking UN legitimacy for piercing national sovereignty, such as in the run-up to the U.S. invasion of Iraq. Today Russia opposed UN intervention in Syria, and I think China does as well.