As the years go by, things just keep getting rougher and rougher for Exeggutor. One of the original RBY superstars, Kantonian Exeggutor has fallen to the depths of obscurity. Grass Psychic is a notoriously poor typing, with many, many common weaknesses. Furthermore, Exeggutor is rather slow and its bulk is now considered average at best, making it difficult to accomplish anything aside from fainting quickly.
Exeggutor has a few things still going for it. It has the highest Base offensive stat of any Chlorophyll user and while not unoutspeedable, being able to outspeed up to unboosted +Natured Base 140 in the Sun with only a Neutral nature is nothing to scoff at. Sleep Powder is another handy tool, allowing Exeggutor disable whatever it can't take out. Of course, there is a reason that Venusaur is the Chlorophyll superstar and Exeggutor is forgotten. Kantonian Exeggutor's coverage is limited to STABs, Sludge Bomb and Ancient Power. Furthermore, no way to further boost its offenses (outside of a random Ancient Power boost) hurts even more. Venusaur's greater bulk and higher speed makes it an even more frustrating Chlorophyll sweeper to take out and is far more unpredictable with its balanced offenses. Being weak to Sucker Punch and First Impression is another unfortunate attribute to have (every Chlorophyll user is weak to Ice Shard, so giving a free pass there) as there are more ways to stop a sweep after it gets started.
Palm Sunny Day
Exeggutor (Kantonian)
Ability: Chlorophyll
Item: Heat Rock
-Sunny Day
-Solar Beam/Energy Ball
-Psyshock
-Sleep Powder/Sludge Bomb
EVs: 4 HP / 252 SATK / 252 SPE
Nature: Modest (+SATK, -ATK)
Basic barebones Sunny Day sweeper. Sunny Day gets Exeggutor going, and as it has no Fire moves it must setup Sunny Day or rely on a team mate to set it up (and with any Dynamax user with a Water, Rock or Ice move able to change the weather, best for Exeggutor to setup its own Sun). Solarbeam is a phenomenal Grass STAB, but gets ruined by any weather change, so Energy Ball is far more reliable. Psyshock is a good secondary STAB and ensures that Exeggutor isn't blanked by Assault Vest users and special sponges not named Mandibuzz or Umbreon. Sleep Powder enables Exeggutor to shutdown any counter that may try to stop it, while Sludge Bomb provides additional anti Grass and Fairy coverage.