You are seriously underestimating the sweeping potential that Chlorophyll alone gives. Let me give you an example... Stoutland. Take a look at this Pokemon. Without any playing experience, there is no way in the world that you would think that this Pokemon would make for a decent sweeper or cleaner in OU, but in reality it does, even with a mediocre Attack stat of 100. The CAP doesn't need many things to derail to the offensive role instead of the defensive with Chlorophyll, if we give it at least a decent Attack stat. Even with just its STABs, HP Fire, and Rapid Spin and LO or lefties, it will make a very good offensive Pokemon even with only 100 Atk and 70 SpA. And don't start listing me examples of what can wall it, as this is not the point. The point is that the CAP would be able to hit hard and outspeed a lot of stuff, while still hitting the Steel-types that are supposed to counter it with HP Fire. It may not be the best offensive Pokemon around, but it will surely make for a good offensive combo with Venusaur. As you can see it is not so easy to avoid going on the offensive with an ability so offensive natured and this is the problem. Even Tangrowth of all things uses offensive Chlorophyll sets over defensive Chlorophyll sets the few times that it sees use on sun teams. And he has 50 Base fucking Speed.
I bet Stoutland would be close to useless without Superpower, Wild Charge, Fire / Ice Fang, and Pursuit. Stoutland is effective because it has an usable Attack stat with very good coverage; since in the threat discussion it was agreed upon (I think) to not give it much coverage, your example is not overly convincing to me. We can tune the stats of CAP5 to reduce the Hidden Power viability on it quite easily, if we don't want it to be able to deal with walls.
I will say it to you once again because you don't get it or because you choose to ignore it on purpose. There are many ways that the CAP can counter Lati@s in rain if we go with Harvest! Be it with decent special bulk (90 HP / 90 SpD) and Sitrus Berry, with great Speed, good Special bulk (95 HP / 110 SpD / 115 Spe) and LumRest, with decent special bulk, good Attack and Speed and Salac Berry (110 Atk / 90 HP / 90 SpD / 100 Spe), or finally with huge special bulk (100 HP / 140 SpD) and LumRest, it can be done! Please do the calcs about the examples i gave you and don't bring up again the ''with Harvest the CAP can't counter Latios without huge special bulk'' argument as it is false. So between countering Lati@s in sun and only checking them in rain and sand with Chlorophyll and countering them in every weather, which would you choose? The winner is obvious, Harvest!
This is not really aimed to counter your argument, but are we really willing to give CAP a 115 Speed stat, Pursuit, and Rapid Spin? Looks really a perfect Spinning machine to me...that even ignoring the ability it's very attractive for every team based around SR removal (not necessarily Sun). I would think twice before using weird stat arrays just to grant CAP5 the ability to run LumRest, since we could end up breaking other aspects of the pokemon that have seen a lower amount of discussion. This is not against Harvest, just I'd be more careful before proposing or even considering an unconditional base 115 Spe in your examples.