i definitely believe that if either rain or sun is banned, the other will have to accompany it into the void. these two are really the most powerful weathers by far. sun has chlorophyll, fire nukes, we all know how this works. rain has hurricane, thunder, hydro pump, etc etc.
however i don't know if sand will need to be banned, if those two are banned - that's a different story altogether, i think. the main use of sand is to get use out of tyranitar while simultaneously annoying other weathers. there are only two mons in OU that are rock (can abuse for sdef boosts), one relevant mon with sand force (landorus-I, and physical landorus is not as popular as it used to be... it was once a powerhouse of the BW metagame though) and only one relevant user of sand veil (gliscor. possibly garchomp depending on what the council says). both the viable sand rushers are in lower tiers, which is indicative of how powerful they are in OU. sand is definitely not being run because any one pokemon can become a powerhouse while under it. that might change if it becomes the only major weather though
and hail will definitely need some more work before it becomes an OU threat. really the main reason hail is run right now is for blizzard spam, residual damage (which sand fails to get on many bulky mons) and, reason #1 by far, to change the weather and deny control of it against others. hail will become stronger if all the other weathers disappear, but i have a tough time believing that it will ever dominate. you can't make a team with more than two ice types on it and still maintain a metagame edge. it's just not gonna happen with a type as shitty as ice.
all these thoughts are a long way off though so it's just theory
EDIT
landorus has sheer force, so it doesn't need sand. keldeo doesn't rely on rain to function, and the power drop isn't that great considering +2 hydro pumps will still hurt. volcarona has been used outside of sun and still works nicely, so it doesn't need sun. Rain Therians are the only things will be nuked, but even thundy-t can still fit on volt-switch teams.
you are missing the point that superbadd tried to make. it doesn't matter that these threats will still be powerful, the point is that they are LESS powerful and that means the counter list goes up. whether that's good or bad is up for discussion, but hp ground lum volcarona in sun has NO counters in the game. only checks. take away the sun and the list goes up dramatically.
as for landorus, you missed something important between sheer and sand force: almost nothing in landorus's physical movepool benefits from sheer force. stone edge and earthquake do NOT gain boosts from sheer force. the whole reason landorus was so powerful was good speed and a solid (not extraordinary) base attack, combined with the sand force boost that affected both rock and ground moves. that means its edgequake was a LOT stronger than most base 100 speed mons should have been capable of achieving. sheer force is only usable on special sets which are easily walled and frankly only effective against a narrow bracket of teams - teams that are popular right now, which is why the set itself is popular, but sheer force landorus-I is without a doubt an anti-meta mon, not a meta one. it counters popular threats but will never be one. it lacks the punch and coverage.
weatherless keldeo is really not all that common. even on sand, where keldeo does appear, the main advantage of running it is that you've taken one of rain's most powerful sweepers and put it on your own team, so you can turn rain's own weapons against it. it happens to be solid enough that it can stick up for itself if rain is not present, but it's not exactly a game-demolishing set without its rain backed hydro pumps. it only gets interesting when you give keldeo the rain support. i personally think keldeo is fine either way though - it has lots of counters because of its shit worthless movepool.
Er, without sand, NO ONE will use Excadrill, so Donphan will remain an OU spinner.
lol WHAT? you serious? sand means excadrill can no longer sweep. it is still without a doubt one of the three best spinners in the game. steel typing, high attack, and enough base HP to take a few hits (not many, donphan is bulkier, but the steel typing goes a LOOONG way). go take a look at excadrill's uber analysis. the bulky spinner set is the FIRST one. not the offensive SD set that arguably made it overpowered in OU... the BULKY SLOW ONE. yeah. it's not gonna sweep any time soon, but it still packs plenty of punch, and moreover, it's a usable pokemon with rapid spin - that alone means it will be guaranteed to see usage. i have even seen mold breaker discussed and used seriously in ubers, because bulky excadrill can use it to force out giratina-O (otherwise you can only hurt giratina-O with boosted shadow claws, and there's only so much room in a moveset that already runs rapid spin).
as for tornadus-T counters, chansey is very shaky because you cannot switch in on a superpower - you won't wish/protect fast enough to survive the next two and you have no leftovers to save your ass with protect stalling. nobody in the game should ever be running heatproof bronzong; the main reason to run bronzong is because levitate takes its resistance pattern from solid to ridiculous. otherwise you suddenly become vulnerable to everything running ground/ice or ground/rock coverage, and there's no shortage of those.