Having played devil's advocate so long in this discussion, I'm going to try to present my reasons for Jynx being broken (if it is indeed broken).
- Jynx has very good coverage and it can hit hard on both sides. In three moves it can 2HKO almost the entire tier. Specifically these are the Pokemon in NU that avoid a 2HKO from LO Ice Beam, Psyshock and Focus Blast (taking SR into consideration):
Specially defensive Alomomola,
Specially defensive Gardevoir,
Specially defensive Musharna,
Specially defensive Duosion,
Physically defensive Flareon,
Specially defensive Wartortle.
That is a shocking list (and yes I did all the calculations). The only ones from there that are remotely usable are the first three namely specially defensive Alomomola, Gardevoir and Musharna. Out of those, only Gardevoir and Musharna can think about countering Jynx in that they always avoid a 2HKO, they have reliable healing, they can threaten Jynx back with Shadow Ball or HP [Fighting].
Some Pokemon such as Hypno did not make the list because they do not even make the cut-off for NU! So there's two usable hard counters in all of NU currently.
- Jynx has access to a sleeping move. Lovely Kiss has the 25% miss rate to make Jynx tear her hair out (maybe she needs to get some better chatup lines, or maybe just stop coming onto things...) but 75% is definitely reliable if Focus Blast is reliable.
- Jynx has good speed. Base 95 is a good speed tier for NU. She isn't godly fast but she still outspeeds most of the tier.
None of the above three factors deem something broken, not even two of them in conjunction. But to have all three of them is what takes Jynx right to the edge. Good speed, amazing coverage, and a sleeping move.
And that isn't even Jynx's best set imo. Jynx's best set uses both Lovely Kiss and Substitute in my view, allowing it to set up on a much larger number of things and has a much better chance to keep up a Sub to prevent revenge killing. With just two attacks, Ice Beam and Psyshock/Focus Blast, Jynx still threatens the vast majority of the tier with a 2HKO and in choosing just one move (Psyshock or Focus Blast) Jynx has vastly different counters.
So is there any bad news for Jynx at all? Yes but the list is much shorter.
- Jynx has little special bulk and no physical bulk. Literally touch it with something physical and it dies. Jynx can not really switch-in to anything in NU with any conviction. Yes some moves are easy to predict but the Jynx user must always be aware that one bad move and Jynx could be gone. This also has a consequence on the threats that are faster than Jynx: Jynx is a non-issue for Pokemon faster than Base 95 - Jynx is not able to tank a hit and threaten them back. So Jynx can dominate the Base 95 speed tier and below, but is powerless to everything above this tier.
- Jynx often lacks the power to OHKO things straight off the bat. Despite all the calculations showing the things Jynx can 2HKO with perfect prediction, it surprisingly struggles to OHKO things (and this is not helped by the amount of Sturdy Pokemon that Jynx should be OHKOing lol!). This combined with Jynx's poor bulk means that it needs some support to truly flourish because often if Jynx fails to OHKO something then it's dead. Lovely Kiss saves it somewhat here but the user must be wary of relying on it because one miss and Jynx risks leaving the battle having achieved nothing.
For me these are the main points when it comes to judging Jynx's position in the tier. Jynx is extremely dangerous and pretty much has the tier at its mercy once it comes in. However its frailty and speed tier is holding back some of its destructive potential. If it has 10 more base speed, or could actually tank an attack then it would be over the edge imo.
The lack of counters in NU is another issue, but there could be another side to it. If Jynx really is the unstoppable monster of NU, why haven't people started using some obscure hard counters? Does this mean people haven't deemed Jynx to be broken enough to sink to those depths to find niche counters? After all Bronzong was used in the Garchomp era, and Gastrodon is used now in the rain era when we know they are likely to be lower tier Pokemon if not for their respective niches.
So this is the million (Poke)dollar question. Has the average NU team figured out a way to handle Jynx (its low bulk, its speed tier, its inability to OHKO things)? The lack of dedicated counters suggests that at least people are playing around Jynx for now. Could that be a sign that Jynx has settled into the metagame and its flaws are in fact readily exploited by the average team, thus outweighing its ridiculous offensive potential?
Personally I haven't been in a situation against Jynx where I have thought "god I really couldn't do anything about that", it has always been because of a misplay on my part or a brilliant play on my opponent's that Jynx starts causing serious problems. That makes me lean towards not broken, and I think it will be really interesting to hear what the council's decision is.