Why has OU been relatively stable when the other tiers and OMs seem to have been suspect testing stuff every 3 months? Did OU just get lucky this generation?
OU is the highest usage-based tier, and given that Ubers is OU’s banlist first and foremost it’s why OU is slow to stabilize early on (when broken stuff like Zygarde-C, Blaziken, Deoxys formes, Marshadow, Naganadel, etc. are legal) but slow to destabilize later in a generation since, ideally, there aren’t any bombshells being dropped to shake up the meta late in a generation.
So there are two potential ways OU can remain stable while other tiers destabilize:
Scenario 1:
OU, as the highest usage-based tier, is extremely inclusive: anything in UU, RU, NU, PU, and the unofficial ZU is usable in OU but more often than not it isn’t great in OU. When stuff like Azumarill and Breloom aren’t used in OU, they eventually drop down to UU due to them not making the 3.41% usage statistics required to enter or remain in a tier. And a lower tier like UU is where the lower power levels give them fewer reliable offensive and defensive answers, and metagames ultimately warp around them until they either fall out of favor or are deemed banworthy, as was the case with both Azumarill and Breloom. Azumarill outclassed many other Water-type breakers and its defensive typing was an absolute headache to boot, too, while Breloom forced tons of switches and had the tools to punish them all dearly, and counterplay to those was developed. Flying types grew prominent in the Breloom meta to fight it and its Spore assault back, and Rhyperior grew prominent as an answer to these.
Scenario 2:
The next common situation, instead of “bad in OU but great in UU” is “good in UU but also good in OU.” A fine example of this could be seen in UU SEVERAL times over the course of this generation: some of the top threats in UU, such as Mamoswine as a powerful wallbreaker and Stealth Rocker, Serperior as a powerful sweeper with fantastic utility options to boot, Amoonguss as a blanket check to the broken parts of the UU meta, and Gliscor as an immeasurably-versatile defensive AND offensive threat with countless centralizing and viable sets, all had some sort of niche in OU at some point or another.
Mamoswine rose to OU in-part because of Aim’s Mamoswine TTT and in-part because the ridiculous Ice/ground typing was incredibly anti-meta in light of all the Tapu Koko, Landorus-T, Magearna, Toxapex, Tapu Bulu, Tangrowth, Heatran, and Zygarde teams running around that were torn to shreds by Mamo’s fantastic coverage. It was a counterpick with a valuable niche at the time and rose as a result, but it leaving really hurt Hyper Offensive playstyles that really appreciated its ability to get Stealth Rock up and keep it up by smashing Defoggers that wanted to get rid of Klefki’s precious Spikes. Spikes+Mamoswine+Mega Sharpedo is a ferocious offensive core in UU but without Mamoswine it’s not quite as good.
Serperior was dangerous, versatile, and splashable in UU and was one of the threats to prep for. But an RMT that utilized Serperior’s good utility options and great speed tier helped Serperior get some usage in OU, and it since rose to OU, finds itself on many Hyper Offense teams here, and is showing no signs of stopping courtesy of having the extremely irritating combo of Substitute+Leech Seed, an incredible Speed stat, and the incredible Glare to paralyze everything except Electric types. With this set Serperior can 1v1 anything slower than it that isn’t immune to Leech Seed, often without even needing to directly attack them. Heatran cannot switch in on SubSeed Serperior, for instance, as if it gets either a Substitute, a Leech Seed, or a lucky Glare off it can just stall Heatran out easily. UU lost Serperior and has since adapted to a tier without the snake.
Amoonguss was used to deal with Breloom, Serperior, and some Azumarill variants due to its great bulk, typing, ability, and its surprisingly good offensive stats. If you’re able to check three of the biggest threats in a tier with one set while being viable against other threats you’re automatically good in that tier. It could, however, lure in and beat Heatran with a powerful Assault Vest set with Stomping Tantrum and this niche was prized enough that it rose to OU. I already told you what Azumarill and Breloom did to UU; that’s because Amoonguss left.
Finally there’s Gliscor. The most versatile threat in UU was so prominent that stuff ran Hidden Power Ice over Hidden Power Grass solely to kill Gliscor. It was a staple on Stall teams but could, due to its role compression and movepool, fit basically anywhere. Much of this carried over to OU after it got the Defog+Poison Heal combo and it eventually rose to OU naturally because it did a lot of the same things here as it did in UU. And the tier adapted: stuff ran Hidden Power Grass to all but invalidate Swampert and Rhyperior and Gligar climbed up the UUVR to try to recapture some of what Gliscor did on fatter teams.
Sorry for the extremely long explanation. But hopefully this was the answer you were looking for.