Unfortunately, this really wouldn't have the effect you're hoping for.
If someone is going to make the conscious effort to cheese the ilvl, they'll do so if you give them even the slightest opening to exploit. You can buy an NQ set of 115 left side from ishgard with zero effort, then go to Ul'dah and buy a full set of i28 accessories to get an ilvl of 81 (if my math is correct) - a zero effort low ilvl-CT compliant cheese for a gearset that most players wont bother looking at and if someone ever does ask, can be easily deflected with 'was the best stuff I had'. The thing your fix would accomplish would make it so now instead of using their super synced down gear to make the experience quicker for the rest of the alliance, they're now stuck in sub-par gear and prolonging the instance for the rest of the 23 people. But that person still got their CT and all the new players, players who only have CT unlocked, players doing CT for the MSQ, and random people queuing for alliance roulette can still easily carry them, and does nothing to dis-incentivize from cheesing CT.
The only way to disincentive cheesing for CT is to make the other raids give bonus exp that makes them much more value or drag every raid down to CT's difficulty level that people wont care what they get since it'll all be ultra snoozefest near impossible to wipe steamroll no matter what. Alternatively, forcing strict ilvl syncs that make CT harder than later raids.