And this little thing took him more time than: 1. Kirk and Sulu starting to fall to their deaths, 2. the transporter operator not able to get them, 3. trying several times, 4. Chekov getting his idea, 5. Chekov running to the transporter room, 6. Chekov executing his idea and finally 7. Kirk and Sulu materializing.
If getting the belt took that much time, then the ship is horribly badly designed, because the equipment room has to be on the other side of the ship. That room should be close to, and ideally right next to or even in the transporter room; thus you not having to waste massive amounts of time getting some equipment to beam down when time is of the essence.
So no matter how you cut and past it, the problem still exists.
No, not really.
This takes... what?... a minute, two on screen?
Yes, that would be a VERY long time, considering he didn't even start putting it on until he got back. That means he ran, ran, ran, grabbed the belt, ran, ran, ran, and reached the transporter room and starting putting on the belt.
I, an overweight slow guy, as a 12-year-old, once managed a 400 meter lap in 2 minutes 26 seconds, and like I said, that was one of the slowest rounds of my age group. For a grown Vulcan used to higher gravity and much thinner air, in the 2-3 minutes he had, he could have ran all the way to the other side of the 700-meter super Enterprise, and back to the transporter room.
And that's assuming he ran the whole way instead of using the much faster turbolift. If that equipment room was right next to, or very close to the transporter room, as it would be in a properly designed ship; Spock would not have had to waste 10 seconds running into the equipment room, yanking a belt, and running back out.
And even if Spock arriving after Kirk and Sulu finally managed to get beamed back was not a problem, there's still the problem that Spock had to beam down to get the council and his parents to begin with. A government in exile/hiding must have communications ability at least to someone who uses logic. All Spock should have had to do was contact them and tell them they're ready to beam them out if they get themselves to some place the transporters can get them.
Yeah, but where would have been the drama in that?
Something that is utterly stupid, when noticed, destroys any drama you have attempted to put on screen. So if you can't do something without stupidity, it's best not to do it all. But if you're going with the stupidity, you better make sure it is the only, or one of a tiny few stupid things in your movie; especially before it comes up. That way, being still entirely immersed in the movie, they might miss it. And if they do notice it, they might be willing to forgive you for that one, although if they're honest, they'd still say it is stupid.
If however there's already been multiple stupid things before that to throw your viewers out of the movie, the chances they miss more stupidities are about the same chances a snowflake has in hell. And there are so many stupidities before this one, so many.