Thank you for finally bringing this up. I've been contemplating this suspect for a while, and my ultimate opinion is that Sun in general isn't a problem. The problem comes when you stack dangerous Chlorophyll users on the same team -- and the sheer offensive presence of Bellsprout under sun.To share my opinion, I think sun without bellsprout is manageable (hell maybe even sun with sprout is manageable). I laddered with a team without sprout and it was ok but nothing great. I would rather have more diversity in team archetypes in the metagame so I'm leaning towards no ban.
From the initial few pages of this suspect thread, it seems that only the double Chlorophyll build of Sun is suspect-worthy, but I then considered whether builds without Bellsprout were even problematic for the metagame. Outside of Bellsprout, the main viable partners for Bulbasaur would be Oddish and Exeggute, both of which are rather lackluster. Not only is Oddish rather slow for a Chlorophyll sweeper (26 Speed max, outsped by the fair few 18+ Spe scarfers in the tier), its movepool is less impressive than Bellsprout's, mainly lacking the important Weather Ball for Steel coverage, forcing it to resort to Hidden Power Fire to hit threats such as Pawniard and Grimer-Alola. Exeggute, while sitting at a much more respectable 28 Speed, is considerably weaker than both Oddish and Bellsprout, and lacks the Poison-type nuke that makes double Chloro so dangerous, instead swapping it for a Psychic-type secondary STAB that honestly isn't strong enough. The two sit at C and D ranks on the VR for a reason. While Deerling is another semi-viable Chlorophyll sweeper, it's a physical-based one that really doesn't overlap well with Bulbasaur for the purposes of double Chloro.
240 SpA Oddish Hidden Power Fire vs. 36 HP / 36 SpD Eviolite Grimer-Alola in Sun: 7-9 (28 - 36%)
240 SpA Oddish Hidden Power Fire vs. 0 HP / 116 SpD Eviolite Pawniard in Sun: 14-18 (66.6 - 85.7%)
240 SpA Oddish Acid Downpour (175 BP) vs. 116 HP / 76 SpD Eviolite Vullaby: 16-19 (64 - 76%)
196 SpA Exeggcute Shattered Psyche (175 BP) vs. 212 HP / 76 SpD Eviolite Spritzee: 15-18 (55.5 - 66.6%)
196 SpA Exeggcute Hidden Power Fire vs. 116 HP / 76 SpD Eviolite Vullaby in Sun: 5-7 (20 - 28%)
196 SpA Exeggcute Hidden Power Fire vs. 36 HP / 36 SpD Eviolite Grimer-Alola in Sun: 7-9 (28 - 36%)
196 SpA Exeggcute Shattered Psyche (175 BP) vs. 0 HP / 236 SpD Munchlax: 16-19 (53.3 - 63.3%)
240 SpA Oddish Hidden Power Fire vs. 0 HP / 116 SpD Eviolite Pawniard in Sun: 14-18 (66.6 - 85.7%)
240 SpA Oddish Acid Downpour (175 BP) vs. 116 HP / 76 SpD Eviolite Vullaby: 16-19 (64 - 76%)
196 SpA Exeggcute Shattered Psyche (175 BP) vs. 212 HP / 76 SpD Eviolite Spritzee: 15-18 (55.5 - 66.6%)
196 SpA Exeggcute Hidden Power Fire vs. 116 HP / 76 SpD Eviolite Vullaby in Sun: 5-7 (20 - 28%)
196 SpA Exeggcute Hidden Power Fire vs. 36 HP / 36 SpD Eviolite Grimer-Alola in Sun: 7-9 (28 - 36%)
196 SpA Exeggcute Shattered Psyche (175 BP) vs. 0 HP / 236 SpD Munchlax: 16-19 (53.3 - 63.3%)
I believe that Sun has a strong foothold in the metagame right now, and players should be expected to deal with its threats in teambuilding like any other offensive threat. However, I don't think Sun as a whole is broken -- only a small part of the playstyle (Bellsprout + Bulbasaur double Chloro sun, which is basically a single team) is even maybe problematic for the metagame. As such, I don't think banning Vulpix and by extension Sun as a playstyle is the way to go for dealing with sun.
Honestly, dealing with weather sweepers has always been weird. Often the Pokemon isn't actually broken alone, but the presence of an external set-up can push it over the edge. See: BW Kingdra (and other SSers), BW Excadrill, BW Garchomp to an extent (Sand Veil). This begs the question, is it enough to suspect the Pokemon for being broken under certain circumstances, or should the one responsible for the set-up that breaks the 'mon in question be suspected instead? It doesn't help that the generation where weather was the most prominent was inconsistent with its bans. Kingdra/Rain was dealt with through a complex Drizzle + Swift Swim ban, Sand was dealt with by simply banning Excadrill, and Garchomp just lost Sand Veil. None of those 'mons (save perhaps Chomp) were particularly strong by themselves, without their respective weathers. More recently, Baton Pass has been a point of contention in other tiers, and is similar in that an external force sets up an otherwise manageable 'mon to overpowered levels. However, Baton Pass can also be seen as an entirely different beast in that its possible recipients are far more abundant than weather abusers. In any case, tiers are also undecided on this issue: OU has a clause where Speed + another stat cannot be simultaneously passed, whereas UU (and by extension lower tiers) banned the move outright.
In this case of dual Chloro being oppressive, would it be a viable option to simply nerf the playstyle similarly to how BW nerfed Sand offense by banning its strongest abuser -- in this case, by looking to suspect Bellsprout instead of Vulpix -- instead of eliminating the archetype as a whole? The effects of Sun are contained to only its abusers (Chlorophyll primarily, and to a lesser extent offensive Fire-types), and really only a small portion of those abusers are even viable, let alone suspect-worthy.