I still think Exeggutor doesn't need a ban. Let's go over everything..
Is it overcentralizing?
No. Common balance teams can beat Egg simply by running pokemon that outspeed it. Of these there are quite a few- Monferno, Zebstrika, Rapidash, Stoutland, Ursaring, Dodrio...the list is endless. Unlike a fat pokemon with few weaknesses like Stoutland, almost everything that outspeeds Eggy can OHKO it.
The only teams it is overcentralizing for is stall, obviously. Eggy forces stall teams to run Zweilous or Vullaby a lot of the time. It can also be beat by the combination of Audino and Gourgeist-Super, but that requires an enormous amount of smart thinking from the stall player's part.
However, is it really any more overcentralizing than other big threats? Sub Will-O and Life Orb Pain Split Rotom-F are incredibly threatening to stall and semi-stall teams. If stall wants to beat those Rotom-F sets it has to run stuff like SpD Grumpig as well as stuff like SpD Camerupt. Nasty Plot Raichu is a ridiculous threat that only needs Stunfisk slightly weakened if running Focus Blast to sweep, and only needs Machoke practically requires stall to run Gourgeist-Super as Ice Punch and Thunderpunch respectively can bop Pelipper and Altaria on the switch.
Is it overpowered?
No, and I don't think anyone thinks it is. Exeggutor, as said previously has a ton of offensive checks that fit on nearly every team. It is tough for it to get more than one kill per match vs most teams. Even when Exeggutor gets a chance to get multiple kills, vs a Stunfisk or vs a Mr.Mime locked into Psychic, for example, it still has to make enormous predictions. Can't necessarily use Giga or Leaf Storm, because what about that Sap Sipper Zebstrika or Sawsbuck, or that Monferno. But if you use Psychic, Pawniard or Signal Beam Grumpig might come in. It's very important for people to understand that
Exeggutor does not have Tinted Lens.
Is it unhealthy?
A bit. There's no denying that Exeggutor lessens the viability of defensive teams. But it is just a medium-small part of a huge surge of pokemon that lead the tide against them that includes Rotom-F, Ursaring with SD, everything with Nasty Plot, and Pawniard. Eggy forces defensive teams to adapt, but it isn't necessarily a huge adaptation they have to make. Vullaby and Zweilous are already two pokemon that fit on a good amount of defensive teams. Gourgeist-Super, which walls Life Orb and Berry sets that use Psyshock, is an easy fit for defensive teams along with Audino. Audino can scout Eggy's sets and then switch out to an appropriate answer, and can even wall a few sets. Defensive teams are already capable of handling Eggy, and even though it is somewhat of a strain, it can be done.
...and despite Exeggutor's presence, defensive teams have more viability in the meta then they ever had since Poliwrath's departure. This is undeniable. Why are we trying to ban Exeggutor when defensive teams have only improved? And do we even have an obligation to preserve stall as a playstyle?
It could even be argued that Exeggutor is healthy in some ways. It stops Stunfisk spam on every team, and punishes people for using it to fish for Static para vs everything. Faster Sleep Powder versions help vs the VERY CENTRALIZING lead Golem. Exeggutor is also one of the best Machoke answers out there, especially Colbur variants, and Machoke is an unhealthy pokemon in the meta.
Is it too versatile?
Does it have too many sets to counter, which means it is too difficult to prepare for? No. Eggy may have many sets, but each of them comes with heavy weaknesses. Choice Specs has to be locked into a move, and both STABs have many pokemon that can take advantage of it. Life Orb sets have the cost of being worn down quickly. Berry sets may provide some utility against offensive teams (Yache Berry counters Floatzel and other waters, while Colbur and Occa respectively let it survive vs Fire Types and Dark Types). However, they are not powerful and a non-threat to defensive teams, which is the whole reason Eggy is being suspected.
Does it fit on too many teams?
Nope. Exeggutor is not all that splashable. On offense, the most common archetype, it brings an enormous amount of weaknesses that are hard to account for (because you don't want to run defensive pokemon) and causes an inherent weakness to faster pokemon. On balance, the same problem applies because much of the team has to be built around Eggy, covering its weaknesses to Fire, Flying, Bug, etc.
Does it beat good teams in the meta?
Here, I'll take 4 very well known and strong teams in the meta and see how they match-up against Exeggutor- but not only that, if they can match up adequately against Exeggutor without resorting to forced strategies and gimmicks to counter it. Although this is purely anecdotal, it will still give you a good idea how teams don't have to go out of the way to deal with Eggy.
1. Dodmen's HO Electric Body
http://www.smogon.com/forums/threads/electric-body.3557821/
Being a hyper offense team, dodmen's team deals with Exeggutor well. Venipede sets up spikes to pressure it. Relicanth can take out a slightly weakened Eggy with Life Orb Head Smash and Jolly Nature, Purugly and Zebstrika both KO it (and Zebstrika bluffs Sap Sipper to get it from spamming grass STAB as well). Mr.Mime loses to it 1v1 unless it is very weakened, but Drifblim sets up Subs on it until it gets into Liechi range and can sweep.
2. Dundies' balance ¯\_(ツ)_/¯
http://www.smogon.com/forums/threads/¯-_-ツ-_-¯.3558925/
Dundies' team is perhaps
overprepared for Exeggutor, but all of the pokemon on the team serve specific purposes that don't include beating Eggy. Right away, you notice Vullaby walls all Eggy sets without Ancient Power. Vullaby is immune to Sleep Powder and can beat non-Specs sets 1v1. Roselia outspeeds most Eggy variants and KOs with Sludge Bomb. Scarf Mr.Mime loses, obviously, but Rotom-F beats it if it can hit Blizzard.
3. CSI Miami's stall Tubular Bells
http://www.smogon.com/forums/threads/tubular-bells.3559281/
The most successful stall team in the meta does not have a dediated Exeggutor answer. And yet, I've played against it several times including once with an Exeggutor, and it wasn't easy. How does Ranbu do it? He has Audino to scout for Specs Exeggutor and then switch out, regaining HP. If he suspects Sleep Powder and Psyshock, he might go to Gourgeist. He might switch to Grumpig with Signal Beam if he suspects a Psychic move. Overall, Eggy is a big threat to the team but not an absurd one.
4. Raiza's balance Xiangjiao
http://www.smogon.com/forums/threads/xiangjiao.3557869/
Raiza has a strange team, that is perhaps weak to Exeggutor. Stunfisk obviously gives Eggy a free switch in. Audino can switch into most of Exeggutor's attacks but fears Sleep Powder. However, Jumpluff can switch into anything grass and revenge a weakened Eggy. Floatzel needs prior damage to revenge kill Eggy, but won't do anything against Yache variants. Scarf Solrock just loses. Monferno, however revenges Eggy with a powerful U-turn and gains momentum.
Going over these teams and others don't
prove anything. You can still make a team that is weak to Exeggutor. But it is easy to build a team that handles Exeggutor while still using all viable pokemon that serve greater purposes than countering it. It is a part of the metagame, not a threat that you have to tailor a specific pokemon on your team to handle, like Vigoroth.
tldr: Exeggutor is not broken vs offense, balance, or stall. There's not much separating it from other powerful wallbreakers such as Rotom-F, Life Orb Mr.Mime, Ursaring, or Life Orb Monferno.
Don't ban